The correct option is B 1 we know that, 1+tan ^2θ= #160; ^2θ Now, tan ^2θ #160; ^2θ=tan ^2θ (1+tan ^2θ)= 1 Therefore, Answer is 1 ...

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Basic Trigonometric Identities

Evaluate: t...

Question

Evaluate: ${tan}^{2} θ - {sec}^{2} θ$

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Solution

The correct option is B $- 1$
we know that, $1 + {tan}^{2} θ = {sec}^{2} θ$

Now, ${tan}^{2} θ - {sec}^{2} θ = {tan}^{2} θ - (1 + {tan}^{2} θ) = - 1$

Therefore, Answer is $- 1$

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{tan}^{2} θ + {cot}^{2} θ + 2 = {sec}^{2} θ + c o s e c^{2} θ

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\frac{1 + {tan}^{2} θ}{1 + {cot}^{2} θ} =

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