Q. 225.0( 2 Votes )

# Mark the correct alternative in the following:

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

A.

B.

C.

D.

Answer :

We know tan^{2}x + 1 = sec^{2}x…(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

⇒ a^{2} – b^{2} = -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}

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