Q3 of 48 Page 84

Prove the following with the help of identities:

cos2θ + cos2θ.cot2θ = cot2θ

Taking L.H.S we get,


cos2 θ + cos2 θ.cot2 θ


⇒ cos2 θ (1 + cot2 θ)


⇒ cos2 θ (1 + )


⇒ cos2 θ ()


Using the identity: 1 + tan2 θ = sec2 θ


⇒ cos2 θ () =


⇒ = cot2 θ


= R.H.S


Hence, proved.


More from this chapter

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1

Express all the trigonometric ratios ∠θ in terms of sec θ.

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Express the trigonometric ratios sin θ, sec θ, tan θ in terms of cot θ.

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Prove the following with the help of identities:

sec θ (1 – sin θ) (sec θ + tan θ) = 1

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Prove the following with the help of identities:

cosec2θ + sec2θ = cosec2θ sec2θ