Question

If 5 cos theta =7 sin theta, find the value of 7sin teta+5cos teta/5sin teta+7cos teta

Answer 1

5cosθ=7sinθ
squaring both sides,
25cos²θ=49sin²θ
or, 49sin²θ=25(1-sin²θ)  [∵, sin²θ+cos²θ=1]
or, 49sin²θ+25sin²θ=25
or, 74sin²θ=25
or, sin²θ=25/74
or, sinθ=5/√74 (neglecting the negative sign)
∴, cos²θ²=1-sin²θ=1-25/74=(74-25)/74=49/74
or, cosθ=7/√74
∴, (7sinθ+5cosθ)/(5sinθ+7cosθ)
=(7×5/√74+5×7/√74)/(5×5/√74+7×7/√74)
=(35/√74+35/√74)/(25/√74+49/√74)
=(70/√74)/(74/√74)
=70/74
=35/37

Answer 2

Hello!!!

Hope this answer would really help you!!!

This is a much easier method to learn too!!!

Thank you!!!