Solution - Trigonometric Identities

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Prove the following identities:

( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2

(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A

( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )

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If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1

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"If "\frac{\cos \alpha }{\cos \beta }=m\text{ and }\frac{\cos \alpha }{\sin \beta }=n " show that " (m^2 + n^2 ) cos^2 β = n^2

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Prove the following identities, where the angles involved are acute angles for which the expressions are defined

(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)

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Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

sqrt((1+sinA)/(1-sinA)) = secA + tanA

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Reference Material

Solution for concept: Trigonometric Identities. For the course 8th-10th CBSE
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