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((sinA-sinB)/(cosA+cosB))+((cosA-cosB)/(sinA+sinB))

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((sinA-sinB)/(cosA+cosB))+((cosA-cosB)/(sinA+sinB))

Posted by Kirti Rane 2 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 2 years, 3 months ago

$\begin{aligned} & \text { LHS }=\frac{\sin A-\sin B}{\cos A+\cos B}+\frac{\cos A-\cos B}{\sin A+\sin B} \\ & =\frac{\sin ^2 A-\sin ^2 B+\cos ^2 A-\cos ^2 B}{(\cos A+\cos B)(\sin A+\sin B)} \\ & =\frac{\left(\sin ^2 A+\cos ^2 A\right)-\left(\sin ^2 B+\cos ^2 B\right)}{(\cos A+\cos B)(\sin A+\sin B)} \\ & =(\cos A+\cos B)(\sin A+\sin B) \\ & =0=\text { RHS } \end{aligned}$

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