3. If
If (* sin o - cos e)
os 0) = 1 and
(cos 0 + sin e) =
y b
b
1, prove that
x y²
62
= 2.
92
Answers
Answered by
1
Answer:
Given sin(θ+α)=a⟹cos(θ+α)=
1−a
2
sin(θ+β)=b⟹cos(θ+β)=
1−b
2
cos(α−β)=cos(θ+α−(θ+β))=cos(θ+α)cos(θ+β)+sin(θ+α)sin(θ+β)=
(1−a
2
)(1−b
2
)
+ab
cos
2
(α−β)=(1−a
2
)(1−b
2
)+a
2
b
2
+2ab
(1−a
2
)(1−b
2
)
=1−a
2
−b
2
+2a
2
b
2
+2ab
(1−a
2
)(1−b
2
)
So
2cos
2
(α−β)−1−4abcos(α−β)
=2−2a
2
−2b
2
+4a
2
b
2
+4ab
(1−a
2
)(1−b
2
)
−1−4a
2
b
2
−4ab
(1−a
2
)(1−b
2
)
=1−2a
2
−2b
2
Answered by
1
Explanation:
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