If tan 15 2 v3 the value of tan 15 cot 75 tan 75 cot 15 is ........

Quantitative Aptitude (CGL) Trignometry

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If tan 15 = 2 - v3 , the value of tan 15. cot 75 + tan 75. cot 15 is.

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Explanation:

tan 15o . cot 75o + tan 75o . cot 15o
= tan 15o . cot (90o - 15o) + tan (90o - 15o) cot 15o
= tan 15o . tan 15o + cot 15o . cot 15o
= (tan 15o)^2 + (cot 15o)^2
= (tan 15o)^2 + 1 / (tan 15o)^2
Putting the value of tan 15o = 2 - v3
= (2 - v3)^2 + (1 / 2 - v3)^2
= (2 - v3)^2 + [(1 / 2 - v3)(2 + v3 / 2 + v3)^2
= (2 - v3)^2 + [(2 + v3) / (4 - 3)]^2
= (2 - v3)^2 + (2 + v3)^2
= 2[2^2 + (v3)^2]
[ (a + b)^2 + (a - b)^2 = 2(a^2 + b^2)]
= 2(4 + 3) = 2 x 7 = 14