Cos2 - - cos2 90 - - - -

The correct option is A 1As cos (90 θ)=sinθ ⇒cos^2θ +sin^2θ =1 ⇒ (A) . ...

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Algebra of Derivatives

Cos2 θ + cos2...

Question

$C o s^{2} θ + c o s^{2} (90 - θ)$ = ?

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c o s e c^{2} (90^{\circ} - θ) - t a n^{2} θ = c o s^{2} (90^{\circ} - θ) + c o s^{2} θ

s e c^{2} θ - c o t^{2} (90^{\circ} - θ) = c o s^{2} (90^{\circ} - θ) + c o s^{2} θ .

$\frac{1 + s i n (90^{\circ} - θ) - {c o s}^{2} (90^{\circ} - θ)}{c o s (90^{\circ} - θ) [1 + s i n (90^{\circ} - θ)]} =$

\frac{1 + cot θ}{1 - cot θ} + \frac{1 - cot θ}{1 + cot θ} = \frac{2}{{sin}^{2} θ - {cos}^{2} θ}

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

(ii) $\frac{s e c θ - t a n θ}{s e c θ + t a n θ} = \frac{c o s^{2} θ}{(1 + s i n θ)^{2}}$

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