\frac{cot \left(\right. 90 º - \theta \left.\right) \cdot sin \left(\right. 90 º - \theta \left.\right)}{sinθ} + \frac{cot 40 º}{tan 50 º} - \left(\right. \left(cos\right)^{2} 20 º + \left(cos\right)^{2} 70 º \left.\right) = ?

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

$\frac{\cot (90 º - θ) \cdot \sin (90 º - θ)}{sinθ} + \frac{\cot 40 º}{\tan 50 º} - (\cos^{2} 20 º + \cos^{2} 70 º) = ?$

–1

None of these

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Given expression $= \frac{tanθ \cdot cosθ}{sinθ} + \frac{\cot 40 º}{\tan (90 º - 40 º)} - {\cos^{2} 20 º + \cos^{2} (90 º - 20 º)}$

$= \frac{sinθ}{cosθ} \cdot \frac{cosθ}{sinθ} + \frac{\cot 40 º}{\cot 40 º} - {\cos^{2} 20 º + \sin^{2} 20 º} = 1 + 1 - 1 = 1 .$