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Let x = (1 + {A})(1 + {B})(1 + {C}), y = (1 - {A})(1 - {B

Question

Let $x = (1 + sin A) (1 + sin B) (1 + sin C), y = (1 - sin A) (1 - sin B) (1 - sin C)$ and If $x = y$ then

x = cos A cos B cos C

y = sin A sin B sin C

y = - cos A cos B cos C

x = - sin A sin B sin C

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Liam Discussed

Let

x = (1 + sin A) (1 + sin B) (1 + sin C), y = (1 - sin A) (1 - sin B) (1 - sin C)

and If

x = y

then

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Given :

x = (1 + sin A) (1 + sin B) (1 + sin C)

.......

(i)

and

y = (1 - sin A) (1 - sin B) (1 - sin C)

.......

(ii)

On multiplying both the equation we get

x y = (1 - sin^{2} A) (1 - sin^{2} B) (1 - sin^{2} C)

∴ x y = cos^{2} A cos^{2} B cos^{2} C

x = y,

then

x^{2} = cos^{2} A cos^{2} B cos^{2} C

⟹ x = \pm cos A cos B cos C

⟹ y = \pm cos A cos B cos C

Hence, option A and C are correct.

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Question Text	Let $x = (1 + sin A) (1 + sin B) (1 + sin C), y = (1 - sin A) (1 - sin B) (1 - sin C)$ and If $x = y$ then
Answer Type	Text solution:1
Upvotes	150