Question

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)`

Answer 1

`log_b(sint)=x`
`sint=b^x`
`sin^2t+cos^2t=1`
`cos^2t=1-sin^2t`
`cos^2t=1-(b^x)^2`
`cost=sqrt(1-c^(2x))`
`log_acost=log_bsqrt(1-b^(2x))`
Option C is correct.