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Solution - Trigonometric Identities

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Question

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

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

`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA`

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If (secA + tanA)(secB + tanB)(secC + tanC) = (secA – tanA)(secB – tanB)(secC – tanC) prove that each of the side is equal to ±1. We have,

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If acosθ – bsinθ = c, prove that asinθ + bcosθ = `\pm \sqrt{a^{2}+b^{2}-c^{2}`

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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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Choose the correct option. Justify your choice.

9 sec2 A − 9 tan2 A =

(A) 1

(B) 9

(C) 8

(D) 0

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