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If b >1,sint >0,cost >0a n d(log)b(sint)...

If `b >1,sint >0,cost >0a n d(log)_b(sint)=x ,t h e n(log)_b(cost)` is equal to `1/2(log)_b(a-b^(2x))` (b) `2log(1-b^(x/2))` `(log)_bsqrt(1-b^(2x))` (d) `sqrt(1-x^2)`

A

`1/2log_b(1-b^(2x))`

B

`2log(1-b^(x//2))`

C

`log_bsqrt(1-b^(2x))`

D

`sqrt(1-x^2)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`log_bsin_t=xorsint=b^x`
Let `log_b(cost)=y,then b^y=cost`
`or b^(2y)=cos^2t=1-sin^2t=1-b^(2x)`
`or 2y=log_b(1-b^(2x))`
`or y=1/3log_b(1-b^(2x))=log_bsqrt(1-b^(2x))`
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