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Question
Find the value of the following:
`((cos 47^circ)/(sin 43^circ))^2 + ((sin 72^circ)/(cos 18^circ))^2 - 2cos^2 45^circ`
Solution
cos 45° = `1/sqrt(2)`
`(cos47^circ)/(sin43^circ) = (cos(90^circ - 43^circ))/(sin43^circ) = (sin43^circ)/(sin43^circ)` = 1 ...[cos (90 − θ) = sin θ]
`(sin72^circ)/(cos18^circ) = (cos(90^circ - 18^circ))/(cos18^circ) = (cos18^circ)/(cos18^circ)` = 1 ...[sin (90 − θ) = cos θ]
`((cos47^circ)/(sin43^circ))^2 + ((sin72^circ)/(cos 18^circ))^2 - 2cos^2 45^circ`
= `1^2 + 1^2 - 2(1/sqrt(2))^2`
= `1 + 1 - 2(1/2)`
= 2 – 1
= 1
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