q If cosp = p' q cos³-psin³ q cos³ +psin³ o q cos³ p-psin³ q cos³ +psin³ p (A) q³ - p³ q³ + p (C) q¹ + pª qª-p4 11 find the value of / यदि cose : q р है तो का मान ज्ञात कीजिए। (B) q³+p³ q³ - p³ q¹ - pª (D) a + pª C
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Step-by-step explanation:
Given, sinθ+cosθ=p, sin
3
θ+cos
3
θ=q
We know a
3
+b
3
=(a+b)(a
2
+b
2
−ab)
Therefore, sin
3
θ+cos
3
θ=(sinθ+cosθ)(sin
2
θ+cos
2
θ−sinθcosθ)
q=p(1−sinθcosθ)
p
q
=1−sinθcosθ
∵sinθ+cosθ=p
1+2sinθcosθ=p
2
2sinθcosθ=p
2
−1
sinθcosθ=
2
p
2
−1
⇒
p
q
=[1−
2
(p
2
−1)
]
⇒2q=p(2−p
2
+1)
⇒2q=p(3−p
2
)
⇒p(p
2
−3)=−2q
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