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Prove the following identities: (sinthe...

Prove the following identities: `(sintheta+cos e ctheta)^2+(costheta+sectheta)^2=7+tan^2theta+cot^2theta`

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`L.H.S ``=(sin theta+{cosec} theta)^{2}+(cos theta+sec theta)^{2}`

`=sin ^{2} theta+{cosec}^{2} theta+2 sin theta {cosec} theta+cos ^{2} theta quad+sec ^{2} theta+2 cos theta sec theta `

`=(sin ^{2} theta+cos ^{2} theta)+{cosec}^{2} theta+2 sin theta times frac{1}{sin theta} +sec ^{2} theta+2 cos theta times frac{1}{cos theta} `

`=1+(1+cot ^{2} theta)+2+(1+tan ^{2} theta)+2`

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RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
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  16. Prove the following identity: (secA secB + tanA tanB)^2 - (secA tanB+ ...

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  17. Prove the following identity: (costheta)/(1-sintheta)=(1+costheta+sint...

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  18. Prove the following identity: (tan^3theta)/(1+tan^2theta)+(cot^3theta)...

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