How do you evaluate $cos ({csc}^{- 1} (\frac{2 \sqrt{2}}{5}))$ $cos(csc^-1((2sqrt2)/5))$ without a calculator?

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Answer 1 · 2016-09-07T04:55:40

Invalid expression.

Let #a = csc^(-1)((2sqrt 2)5) in Q1, for the principal value, wherein

cosine is positive. Then,

csc a =(2 sqrt 2)/5. The reciprocal sin a = 5/(2sqrt 2) = 1.76... > 1.

And so, a is unreal. The given expression is invalid..

How do you evaluate cos(csc^-1((2sqrt2)/5))cos(csc−1(2√25))cos(csc^-1((2sqrt2)/5)) without a calculator?