⇒ tan^2 θ sin^2 θ =sin^2 θ/cos^2 θ sin^2 θ = sin^2 θ sin^2 θ cos^2 θ/cos^2 θ =sin^2 θ(1 cos^2 θ)/cos^2 θ =sin^2 θ/cos^2 θ.sin^2 θ =tan^2 θ sin^2 θ ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identities

tan2 θ-sin2 θ...

Question

$t a n^{2} θ - s i n^{2} θ =$

s e c^{2} θ . s i n^{2} θ

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t a n^{2} θ . c o s^{2} θ

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s i n^{2} θ . c o t^{2} θ

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t a n^{2} θ . s i n^{2} θ

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Solution

The correct option is D $t a n^{2} θ . s i n^{2} θ$
$\Rightarrow t a n^{2} θ - s i n^{2} θ$

$= \frac{s i n^{2} θ}{c o s^{2} θ} - s i n^{2} θ$

$= \frac{s i n^{2} θ - s i n^{2} θ c o s^{2} θ}{c o s^{2} θ}$

$= \frac{s i n^{2} θ (1 - c o s^{2} θ)}{c o s^{2} θ}$

$= \frac{s i n^{2} θ}{c o s^{2} θ} . s i n^{2} θ$

$= t a n^{2} θ s i n^{2} θ$

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, then

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.............

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tan2 θ−sin2 θ=

The correct option is D tan2θ.sin2θ⇒tan2 θ−sin2 θ =sin2 θcos2 θ−sin2 θ =sin2 θ−sin2 θ cos2 θcos2 θ =sin2 θ(1−cos2 θ)cos2 θ =sin2 θcos2 θ.sin2 θ =tan2 θ sin2 θ

$t a n^{2} θ - s i n^{2} θ =$