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Prove the following trigonometric identities: Prove that: (i) √sec θ−1sec θ+1+√sec θ+1sec θ−1=2 cosec θ (ii) √1+sin θ1−sin θ+√1−sin θ1+sin θ=2 cosec θ (iii) √1+cos θ1−cos θ+√1−cos θ1+cos θ=2 cosec θ (iv) sec θ−1sec θ+1=(sin θ1+cos θ)2 |
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Answer» Prove the following trigonometric identities: Prove that: (i) √sec θ−1sec θ+1+√sec θ+1sec θ−1=2 cosec θ (ii) √1+sin θ1−sin θ+√1−sin θ1+sin θ=2 cosec θ (iii) √1+cos θ1−cos θ+√1−cos θ1+cos θ=2 cosec θ (iv) sec θ−1sec θ+1=(sin θ1+cos θ)2 |
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