if sin theta + cos theta = a and sin theta+ cos theta/ sin theta cos theta=b find
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Answer:
Given, secθ+cscθ=b and sinθ+cosθ=a
⇒
sinθ
1
+
cosθ
1
=b
⇒
sinθcosθ
sinθ+cosθ
=b
⇒
sinθcosθ
a
=b
⇒sinθcosθ=
b
a
--- [1]
Now consider, sinθ+cosθ=a
Squaring on both the sides we get,
(sinθ+cosθ)
2
=a
2
⇒sin
2
θ+cos
2
θ+2sinθcosθ=a
2
⇒1+
b
2a
=a
2
----[From1]
⇒
b
(b+2a)
=a
2
⇒(b+2a)=a
2
b
⇒2a=a
2
b−b
⇒2a=b(a
2
−1)
Hence, the answer is 2a.
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