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Q-5 Evaluate: \[ \frac{\tan 20^{\circ}}{\cot 70^{\circ}}+\frac{\cot 50^{\circ}}{\tan 40^{\circ}}+\frac{\sin ^{2} 20+\sin ^{2} 70}{\sin \theta \cdot \cos (90-\theta)}+\cos (\theta \cdot \sin (00-\theta) . \] |
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Answer» \(\frac{tan20^o}{cot 70^o}+\frac{cot 50^o}{tan 40^o}+\frac{sin^220^o+sin^270^o}{sin\theta cos(90^o-\theta)}\) + cos θ sin (90°- θ) = \(\frac{tan20^o}{cot(90^o-20^o)}+\frac{cot(90^o-40^o)}{tan40^o}\) + \(\frac{sin^220^o+sin^2(90^o-20^o )}{sin\theta.sin\theta}\) + cos θ. cos θ (∵ sin (90° - θ) - cos θ, cos(90° - θ) = sin θ ) = \(\frac{tan20^o}{tan 20^o}+\frac{tan 40^o}{tan 40^o}+\frac{sin^220^o+cos^220^o}{sin^2\theta}\) + cos2 θ (∵ cot (90° - θ) = tan θ, & sin (90° - θ) = cos θ ) = 1 + 1 + \(\frac1{sin^2\theta}+cos^2\theta\) ( ∵ sin2θ + cos2θ = 1) = 2 + cosec2 θ + cos2 θ ( ∵ \(\frac1{sin\theta}\) = cosec θ) |
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