If sinA = 4/5 And cosB = 5/13, where 0 <A, B < π/2, find the values of the following:

(i) sin(A +B)

(ii) cos(A +B)

(iii) sin(A –B)

(iv) cos(A -B)

If SinA = 12/13 And sinB = 4/5, where π/2<A < π And 0 <B < π/2, find the following:

(i) sin(A +B) (ii) cos(A +B)

If sinA = 3/5, cosB = –12/13, where A And B Both lie in second quadrant, find the value of sin(A +B).

If cosA = – 24/25 And cosB = 3/5, where π <A < 3π/2 And 3π/2 <B < 2π, find the following:

(i) sin(A +B) (ii) cos(A +B)

If tanA = 3/4, cosB = 9/41, where π<A < 3π/2 And 0 <B < π/2, find tan(A +B).

If sinA = 1/2, cosB = 12/13, where π/2<A < π And 3π/2 <B < 2π, find tan(A -B).

Evaluate the following:

(i) sin 78⁰ cos 18⁰ – cos 78⁰ sin 18⁰ (ii) cos 47⁰ cos 13⁰ - sin 47⁰ sin 13⁰

(iii) sin 36⁰ cos 9⁰ + cos 36⁰ sin 9⁰ (iv) cos 80⁰ cos 20⁰ + sin 80⁰ sin 20⁰

If cosA = –12/13 and cotB = 24/7, where A lies in the second quadrant and B in the third quadrant, find the values of the following:

(i) sin(A +B) (ii) cos(A +B) (iii) tan(A +B)

Prove that: cos 7π/12 + cos π/12 = sin 5π/12 – sin π/12

Prove that:

Prove that:

(i) ⁽ii)

(ii)

Prove that:

Prove that:

Prove that:

Prove that:

If tanA = 5/6 And tanB = 1/11, prove thatA +B = π/4.

If tanA = m/m–1 And tanB = 1/2m – 1, then prove that A –B = π/4.

prove that:

cos² π/4 - sin²

prove that:

sin²(n + 1)A – sin²nA = sin(2n + 1)A sinA

Prove that:

Prove that:

Prove that:

Prove that:

sin²B = sin²A + sin²(A-B) – 2sinA cosB sin(A-B)

Prove that:

cos²A + cos²B – 2 cosA cosB cos(A +B) = sin²(A +B)

Prove that:

Prove that:

tan 8x – tan6x – tan 2x = tan 8x

tan 6x tan 2x

Prove that:

Prove that:

tan 36⁰ + tan 9⁰ + tan 36⁰ tan 9^{0 =} 1

Prove that:

tan13x – tan 9x – tan 4x = tan 13 x

Tan 9x tan 4x

Prove that:

If , show that .

If tanA = tanB, prove that .

If tan(A +B) = And tan(A -B) = y, find the values of tan 2A And tan 2B.

If CosA + SinB = m And SinA + CosB = n, prove that 2 Sin(A +B) = m² + n² – 2.

If tanA + tanB =A And CotA + CotB =B, prove that: cot(A +B) = 1/a – 1/b.

If lies in the first quadrant And cos x = 8/17, then prove that

If then prove that .

If sin(α + β) = 1 And sin(α – β) = 1/2, where , then find the values of tan(α + 2β) And tan(2α + β).

If α,β are two different values of x lying between 0 And 2π which satisfy the equation 6 cos x + 8 sin x = 9, find the value of Sin(α+β).

If sin α + sin β =A And cos α + cos β =B, show that

(i)

(ii)

Prove that:

Prove that:

Prove that:

If sin α sin β - cos α cos β + 1 = 0, prove that 1 + cot α tan β = 0.

If tan α = x + 1, tanβ = x - 1, show that 2 cot(α - β) = x².

IfAngle θ is divided into two parts such that the tangents of the one part is λ times the tangent of other, And ϕ is their difference, then show that .

If , then show that sin α + cos α = cos x.

If α And β are two solutions of the equation Atanx + Bsecx = c, then find the values of sin(α + β).

Find the maximum and minimum values of each of the following trigonometrical expressions:

(i) 12 sin x- 5 cos x

(ii) 12 cos x + 5 sin x+ 4

(iii)

(iv) sin x – cos x + 1

Reduce each of the following expressions to the Sine And Cosine of A single expression:

Reduce each of the following expressions to the Sine And Cosine ofA single expression:

cos x – sin x

Reduce each of the following expressions to the Sine And Cosine ofA single expression:

24 cos x + 7 sin x

Show that Sin 100⁰ – Sin 10⁰ is positive.

Prove that lies between and .

If α + β - γ = π, and sin² α + sin² β – sin² γ = λ sin α sin β cos γ, then write the value of λ.

Write the maximum and minimum values of 3 cos x + 4 sin x + 5.

Write the maximum values of 12 sin x – 9 sin² x.

If 12 sin x – 9 sin² x attains its maximum value at x = α, then write the value of sin α.

Write the interval in which the values of lie.

If tan (A + B) = p and tan (A – B) = q, then write the value of tan 2B.

If then write the value of tan x tan y.

If then write the value of ab + bc + ca.

If A + B = C, then write the value of tan A tan B tan C.

If sin α – sin β = a and cos α + cos β = b, then write the value of cos (α + β).

If and then write the value of α + β lying in the interval (0, π/2).

Mark the correct alternative in the following:

The value of is

Mark the correct alternative in the following:

If A + B + C = π, then sec A (cos B cos C – sin B sin C) is equal to

Mark the correct alternative in the following:

tan 20^o + tan 40^o + √3 tan 20^o tan 40^o is equal to

Mark the correct alternative in the following:

If and then the value of A + B is

Mark the correct alternative in the following:

If 3 sin x + 4 cos x = 5, then 4 sin x – 3 cos x =

Mark the correct alternative in the following:

If in a ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =

Mark the correct alternative in the following:

tan 3A – tan 2A – tan A is equal to

Mark the correct alternative in the following:

If then is equal to

Mark the correct alternative in the following:

If and where P and Q both are acute angles. Then, the value of P – Q is

Mark the correct alternative in the following:

If cot (α + β) = 0, then sin (α + 2 β) is equal to

Mark the correct alternative in the following:

is equal to

Mark the correct alternative in the following:

The value of is

Mark the correct alternative in the following:

If then

Mark the correct alternative in the following:

If sin (π cos x) = cos (π sin x), then sin 2x =

Mark the correct alternative in the following:

If and then the value of θ + ϕ is

Mark the correct alternative in the following:

The value of cos (36^o – A) cos (36^o + A) + cos (54^o + A) cos (54^o – A) is

Mark the correct alternative in the following:

If tan (π/4 + x) + tan (π/4 – x) = a, then tan² (π /4 + x) + tan² (π /4 – x) =

Mark the correct alternative in the following:

If then the smallest positive value of B is

Mark the correct alternative in the following:

If A – B = π /4, then (1 + tan A) (1 – tanB) is equal to

Mark the correct alternative in the following:

The maximum value of is

Mark the correct alternative in the following:

If and tan A tan B = 2, then

Mark the correct alternative in the following:

If tan 69^o + tan 66^o – tan 69^o tan 66^o = 2k, then k =

Mark the correct alternative in the following:

If and then α + β is equal to