If 5 cos theta=7 sin theta,then find the value of 7 sin theta+5 cos theta upon 5 sin theta+7 cos theta
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5 cos theta = 7
hence cos theta = 5/7
hence 5 = adjacent side
7 = hypotenuse
hence by pythagoras theorem;
5^2 + a^2 = 7^2
=> a^2 = 49 - 25
a = √24 = opposite side
hence (7 sin theta + 5 cos theta)/(5 sin theta + 7 cos theta)
= [7(√24/7) +5(5/7)] / [5(√24/7) +7(5/7)]
= [(7√24 + 25)/7] / [(5√24 + 35)/7]
= (7√24 + 25)/7 x 7/(5√24 + 35)
= (7√24 + 25)/5√24 + 35)
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