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Find the value : sin (50° + θ) — cos (40° — θ) + tan 1° tan 10° tan 80° tan 89°

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answer is B.

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Detailed Solution

Given, sin (50° +θ) — cos (40° — θ) + tan 1° tan 10° tan 80° tan 89°

= sin ((90°- (40° - θ)) — cos (40° — θ) + (tan 1° tan 89°)(tan10° tan 80°)

= cos (40° - θ) - cos (40° - θ) + {tan 1° tan (90°-1°)}{tan10° tan(90°-10°)}

= 0 + {(tan 1° cot 1°}{tan10° cot 10°}

= 0 + 1

= 1.

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