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If A, B, C are the angles of a triangle ...

If A, B, C are the angles of a triangle such that `sin^(2)A+sin^(2)B=sin^(2)C`, then

A

sin A + sin B >1

B

tan A tan B = 1

C

sin A + sin B = 1

D

tan A. tan B < 1

Text Solution

Verified by Experts

The correct Answer is:
A, B
`sin^(2)A+sin^(2)B=sin^(2)C`
`rArr a^(2)+b^(2)=c^(2)`
`rArr C=(pi)/(2)` and `A, B lt (pi)/(2)`
Since `A+B=(pi)/(2) therefore tan A tan B = 1`
Also `sin A gt sin^(2) A, sin B gt sin^(2) B`
`rArr sin A + sin B gt sin^(2) A + sin^(2)B = sin^(2)C = 1`
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