Prove that ( cosec θ - sin θ )(sec θ-cosθ)(tan θ - cot θ) = 1
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Step-by-step explanation:
(cosec θ - sin θ) (sec θ-cosθ) (tan θ - cot θ) = 1
L.H.S => (cosec θ - sin θ) (sec θ-cosθ) (tan θ - cot θ)
= (1-sin²θ)/sin θ × (1-cos²)/cos θ × (tan²θ-1)/tan θ
= sin θ cos θ × (tan²θ-1)/tan θ
= sin θ cos θ × [(sin²θ-cos²θ)/cos θ]/[sin θ cos θ]
= sin θ cos θ × 1/cos²θ × cos θ/sin θ
= 1
R.H.S => 1
∴ L.H.S = R.H.S (Proved)
Hope, it will help you......
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