if 4 x tan 15 cot 36 cot 54 tan 75 is equal to 36 then find the value of x
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the answer of this question is 9
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Answer: 9
Step-by-step explanation:
4x tan15 cot 36 cot 54 tan 75 = 36
=> 4x tan15 tan75 cot36 cot54 = 36
=> 4x tan15 tan(90-15) cot36 cot(90-36) = 36
=> 4x tan15 cot15 cot36 tan36 = 36 [tan(90-θ) = cotθ ; cot(90-θ) = tanθ]
=> 4x tan15 × 1/tan15 × 1/tan36 × tan36 = 36 [cotθ = 1/tanθ]
=> 4x 1 × 1 = 36
=> 4x = 36
=> x = 36/4
=> x = 9
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