5. If sin + sin? 0 = 1, find the value of
cos!2 + 3 cos! +3 cos 0 + cos 0+2 cos4 + 2 cos2 0 - 2
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Answer:
Consider the given data.
sinθ+sin
2
θ=1
sinθ=1−sin
2
θ
sinθ=cos
2
θ
We have,
=cos
12
θ+3cos
10
θ+3cos
8
θ+cos
6
θ+2cos
4
θ+2cos
2
θ−2
=cos
12
θ+3cos
10
θ+3cos
8
θ+cos
6
θ+2(cos
4
θ+cos
2
θ−1)
=(cos
4
θ+cos
2
θ)
3
+2(cos
4
θ+cos
2
θ−1)
Since, sinθ=cos
2
θ
Therefore,
=(sin
2
θ+sinθ)
3
+2(sin
2
θ+sinθ−1)
=1
3
+2(1−1)
=1+0
=1
Hence, the required value is 1.
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