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Which of the following trigonometric statement does hold good?

Question

Which of the following trigonometric statement does hold good?

A

tan (\frac{π}{4} + x) = cot (\frac{π}{4} - x)

B

tan (\frac{π}{4} + x) = \frac{1 + tan x}{1 - tan x}

C

tan (\frac{π}{4} + x) = sec 2 x + tan 2 x

D

all of these

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Text solutionVerified

tan (\frac{π}{4} + x) = tan (\frac{π}{2} - \frac{π}{4} + x) = tan (\frac{π}{2} - (\frac{π}{4} - x)) = cot (\frac{π}{4} - x)

So option

A

is true

tan (\frac{π}{4} + x) = \frac{tan \frac{π}{4} + tan x}{1 - tan \frac{π}{4} tan x} = \frac{1 + tan x}{1 - tan x}

So option

B

is true

tan (\frac{π}{4} + x) = \frac{1 + tan x}{1 - tan x} = \frac{( 1 + tan x ) ^{2}}{( 1 - tan ^{2} x )}

= \frac{( sin x + cos x ) ^{2}}{cos ^{2} x - sin ^{2} x} = \frac{sin ^{2} x + cos ^{2} x + 2 sin x cos x}{cos 2 x} = \frac{1}{cos 2 x} + \frac{sin 2 x}{cos 2 x} = sec 2 x + tan 2 x

So option

C

is true

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Question Text	Which of the following trigonometric statement does hold good?
Answer Type	Text solution:1
Upvotes	150