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Find the value of cot θ tan (90° -θ) - sec (90° - θ)cosec θ +√3tan 12°tan 60°tan 78°.

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Detailed Solution

cot θ tan (90° -θ) - sec (90° - θ)cosec θ +√3tan 12°tan 60°tan 78°

= cot θ cot θ - cosec θ cosec θ +√3 tan 60° tan 12° tan 78°

= cot² θ – cosec² θ +√3 tan 60° tan 12° tan(90-12)°

= - (cosec²θ – cot² θ) +√3 tan 60° tan 12° cot 12°

= - 1 + √3(√3 × 1)

= - 1 + 3

= 2

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