Mark the correct alternative in the following: If tan θ + sec θ = e x , then cos θ equals

Question

Philoid · Accepted Answer

We know tan²x + 1 = sec²x…(1)

Let tan θ be a and sec θ be b

According to question

a + b =e^x

Manipulating and Substituting in 1 we get

⇒ a² – b² = -1

⇒ (a-b)( a + b) = -1

⇒ (a-b).e^x =-1

⇒ a-b = -e^-x

a + b =e^x

a-b = -e-^x

subtracting above equations we get

2b =e^x +e^-x