Sometimes expanding stuffs is very helpful!

Geometry Level 4

Given that A , B , C A, B,C are such real numbers for which all trigonometric functions are defined and tan ⁡ ( A − B ) tan ⁡ ( A ) + sin ⁡ 2 ( C ) sin ⁡ 2 ( A ) = 1 \dfrac{\tan(A-B)}{\tan(A)} + \dfrac{\sin^{2}(C)}{\sin^{2}(A)} = 1 , then the expression tan ⁡ ( A ) ⋅ tan ⁡ ( B ) \tan(A) \cdot \tan(B) is equal to:

c o t 2 ( C ) cot^{2}(C) s i n 2 ( C ) sin^{2}(C) s e c 2 ( C ) sec^{2}(C) t a n 2 ( C ) tan^{2}(C) c o s 2 ( C ) cos^{2}(C) c o s e c 2 ( C ) cosec^{2}(C)

Aditya Sky by Aditya Sky , 21, India

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1 solution

Ahmad Saad
Feb 8, 2016

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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