find the value of theta (theta<90degree ) if cos theta / 1-sin theta + cos theta/1+sin theta equal to 4
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Answer:
Step-by-step explanation:
Consider the given equation.
sinθ+2cosθ=1 ……… (1)
On squaring both sides, we get
(sinθ+2cosθ)
2
=1
2
sin
2
θ+4cos
2
θ+4sinθcosθ=1
We know that
sin
2
θ=1−cos
2
θ
cos
2
θ=1−sin
2
θ
Therefore,
1−cos
2
θ+4(1−sin
2
θ)+4sinθcosθ=1
−cos
2
θ+4−4sin
2
θ+4sinθcosθ=0
−cos
2
θ−4sin
2
θ+4sinθcosθ=−4
4sin
2
θ+cos
2
θ−4sinθcosθ=4
(2sinθ−cosθ)
2
=4
2sinθ−cosθ=2
Hence, proved.
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