Prove the following identities

sec⁴x – sec²x = tan⁴x + tan²x

Prove the following identities

sin⁶x + cos⁶x = 1 – 3 sin²x cos²x

Prove the following identities

(cosecx – sinx) (secx – cosx) (tanx + cotx) = 1

Prove the following identities

cosecx (secx – 1) – cotx (1 – cosx) = tanx – sinx

Prove the following identities

Prove the following identities

= (secx cosecx + 1)

Prove the following identities

Prove the following identities

(secx sec y + tanx tan y)² – (secx tan y + tanx sec y)² = 1

Prove the following identities

Prove the following identities

Prove the following identities

= sinx cosx

Prove the following identities

sin²x cos²x

Prove the following identities

(1 + tan α tan β)² + (tan α – tan β)² = sec² α sec² β

Prove the following identities

= sin²x cos²x

Prove the following identities

Prove the following identities

cosx (tanx + 2) (2 tanx + 1) = 2 secx + 5 sinx

If then prove that is also equal to a.

If find the values of tanx, secx and cosecx

If then find the value of

If show that

If cosecx – sinx = a³, secx – cosx = b³, then prove that a² b² (a² + b²) = 1.

If cotx(1 + sinx) = 4m and cotx(1 – sinx) = 4n, prove that (m² – n²)² = mn.

If sinx + cosx = m, then prove that sin⁶x + cos⁶x = where m² ≤ 2

If a = secx – tanx and b = cosecx + cotx, then show that ab + a – b + 1 = 0.

Prove that :

where

If T_n = sinⁿx + cosⁿx, prove that

If T_n = sinⁿx + cosⁿx, prove that

2 T₆ – 3 T₄ + 1 = 0

If T_n = sinⁿx + cosⁿx, prove that

6 T₁₀ – 15 T₈ + 10 T₆ – 1 = 0

Find the values of the other five trigonometric functions in each of the following:

cot in quadrant III

Find the values of the other five trigonometric functions in each of the following:

cos in quadrant II

Find the values of the other five trigonometric functions in each of the following:

tan in quadrant III

Find the values of the other five trigonometric functions in each of the following:

sin in quatrant I

If sin and lies in the second quadrant, find the value of secx + tanx.

If sin tan and find the value of 8 tan

If sinx + cosx = 0 andx lies in the fourth quadrant, find sinx and cosx.

If cos and find the values of other five trigonometric functions and hence evaluate

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

sin 17 π

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

Find the values of the following trigonometric ratios:

prove that :

tan 225^o cot 405^o + tan 765^o cot 675^o = 0

prove that :

prove that :

cos 24^o + cos 55^o + cos 125^o + cos 204^o + cos 300^o =

prove that :

tan (-225^o) cot (-405^o) – tan (-765^o) cot (675^o) = 0

prove that :

cos 570^o sin 510^o + sin (-330^o) cos (-390^o) = 0

prove that :

prove that :

Prove that :

Prove that :

Prove that :

Prove that :

Prove that :

Prove that :

Prove that :

In a ∆ABC, prove that :

i. cos (A + B) + cos C = 0

ii.

iii.

If A, B, C, D be the angles of a cyclic quadrilateral taken in order prove that :

cs(180^o – A) + cos (180^o + B) + cos (180^o + C) – sin (90^o + D) = 0

Find x from the following equations:

Find x from the following equations:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Write the maximum and minimum values of cos (cos x).

Write the maximum and minimum values of sin (sin x).

Write the maximum value of sin (cos x).

If sin x = cos² x, then write the value of cos² x (1 + cos² x).

If sin x = cosec x = 2, then write the value of sinⁿ x + cosecⁿ x.

If sin x + sin² x = 1, then write the value of cos¹² x + 3 cos¹⁰ x + 3 cos⁸ x + cos⁶ x.

If sin x + sin² x = 1, then write the value of cos⁸ x + 2 cos⁶ x + cos⁴ x.

If sin θ₁ + sin θ₂ + sin θ₃ = 3, then write the value of cos θ₁ + cos θ₂ + cos θ₃.

Write the value of sin 10° + sin 20° + sin 30° + ... + sin 360°.

A circular wire of radius 15 cm is cut and bent so as to lie along the circumference of a loop of radius 120 cm. Write the measure of the angle subtended by it at the centre of the loop.

Write the value of 2 (sin⁶ x + cos⁶ x) − 3 (sin⁴ x + cos⁴ x) + 1.

Write the value of cos 1° + cos 2° + cos 3° + ... + cos 180°.

If cot (α + β) = 0, then write the value of sin (α + 2β).

If tan A + cot A = 4, then write the value of tan⁴ A + cot⁴ A.

Write the least value of cos² x + sec² x.

If x = sin¹⁴x + cos²⁰ x, then write the smallest interval in which the value of x lie.

If 3 sin x + 5 cos x = 5, then write the value of 5 sin x − 3 cos x.

Mark the correct alternative in the following:

Mark the correct alternative in the following:

If , then sec x + tan x =

Mark the correct alternative in the following:

If , then is equal to

Mark the correct alternative in the following:

If π < x < 2 π, then is equal to

Mark the correct alternative in the following:

If , and if , then y is equal to

Mark the correct alternative in the following:

If , then is equal to

Mark the correct alternative in the following:

If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x² + y² + z² is independent of

Mark the correct alternative in the following:

If , then x is equal to

Mark the correct alternative in the following:

If and x lies in the IV quadrant, then the value of cos x is

Mark the correct alternative in the following:

If , then is equal to

Mark the correct alternative in the following:

sin⁶ A + cos⁶ A + 3 sin² A cos² A =

Mark the correct alternative in the following:

If , then cos x is equal to

Mark the correct alternative in the following:

If , then tan x =

Mark the correct alternative in the following:

is true if and only if

Mark the correct alternative in the following:

If x is an acute angle and , then the value of is

Mark the correct alternative in the following:

The value of sin² 5° + sin² 10° + sin² 15° + … + sin² 85° + sin² 90° is

Mark the correct alternative in the following:

Mark the correct alternative in the following:

If tan A + cot A = 4, then tan⁴ A + cot⁴ A is equal to

Mark the correct alternative in the following:

If x sin 45° cos² 60°, then x =

Mark the correct alternative in the following:

If A lies in second quadrant and 3 tan A + 4 = 0, then the value of 2 cot A − 5 cos A + sin A is equal to

Mark the correct alternative in the following:

If , then tan x =

Mark the correct alternative in the following:

If tan θ + sec θ = e^x, then cos θ equals

Mark the correct alternative in the following:

If sec x + tan x = k, cos x =

Mark the correct alternative in the following:

If , the

Mark the correct alternative in the following:

Which of the following is incorrect?

Mark the correct alternative in the following:

The value of cos 1° cos 2° cos 3° ... cos 179° is

Mark the correct alternative in the following:

The value of tan 1° tan 2° tan 3° ... tan 89° is

Mark the correct alternative in the following:

Which of the following is correct?