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Question
Find the value of the following:
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin31^circ) + cos theta/(sin(90^circ - theta))- 8cos^2 60^circ`
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Solution
cos 60° = `1/sqrt(2)`
`(cos 70^circ)/(sin 20^circ) = (cos(90^circ - 20^circ))/(sin 20^circ) = (sin 20^circ)/(sin 20^circ)` = 1
`(cos 59^circ)/(sin 31^circ) = (cos(90^circ - 31^circ))/(sin 31^circ) = (sin 31^circ)/(sin 31^circ)` = 1
`(cos theta)/(sin(90^circ - theta)) = cos theta/cos theta` = 1
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin31^circ) + cos theta/(sin(90^circ - theta))- 8cos^2 60^circ`
= `1 + 1 + 1 - 8(1/2)^2`
= `3 - 8 xx 1/4`
= 3 – 2
= 1
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