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

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answer is C.

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Detailed Solution

Given, 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°

.. {tan (90° - θ) = cotθ , sec (90° - θ) = cosec θ}

= 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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