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Question

If 4sinθ=3 and csc2θcot2θsec2θ1+23cotθ=7x+cosθ, then find the value of x

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Solution

4sinθ=3sinθ=34So,cosθ=74Now,cosec2θcot2θsec2θ1+23cotθ=7x+cosθ1tan2θ+23cotθ=7x+cosθcotθ+23cotθ=7x+cosθ2473=7x+7487=7(1x+14)1x+14=81x=8141x=314x=431

Hence, this is the answer.

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