Question

is 5 cot theta equals to 7 then find 7 sin theta + 5 cos theta divided by 5 sin theta + 7 cos theta​

Answer 1

Answer:

35/37

Step-by-step explanation:

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

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