Prove That: Sin θ Cos ( 90 ∘ − θ ) Cos θ Sin ( 90 ∘ − θ ) + Cos θ Sin ( 90 ∘ − θ ) Sin θ Cos ( 90 ∘ − θ ) - Mathematics

Sum

Prove that:

$\frac{\sin\theta \cos(90^\circ - \theta)\cos\theta}{\sin(90^\circ- \theta)} + \frac{\cos\theta \sin(90^\circ - \theta)\sin\theta}{\cos(90^\circ - \theta)}$

Solution

LHS $\begin{array}{l} = \frac{\sin\theta\cos( {90}^\circ - \theta)\cos\theta}{\sin( {90}^\circ - \theta)} + \frac{\cos\theta\sin( {90}^\circ - \theta)\sin\theta}{\cos( {90}^\circ - \theta)} \\ \end{array}$
$\begin{array}{l}= \frac{\sin\theta\sin\theta\cos\theta}{\cos\theta} + \frac{\cos\theta\cos\theta\sin\theta}{\sin\theta} \\ \end{array}$
$\begin{array}{l}= \sin^2 \theta + \cos^2 \theta \\ \end{array}$
= 1

= RHS

Hence proved.

Concept: Trigonometry
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 7 Trigonometric Ratios of Complementary Angles
Exercises | Q 5.3 | Page 313

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