If `tanA=3/4,cosB=9/(41), w h e r e\ pi

Explanation

Given as tan A = 3/4 and cos B = 9/41, where `pi < A < (3pi)/2` and `0 < B < pi/2`

As we know that, A is in third quadrant, B is in first quadrant.

Therefore, tan function And sine function are positive.

On using the formula,` sin B = sqrt((1 – cos^2 B)) `
Now, let us find the value of sin B.

` sin B = sqrt((1 – cos^2 B))`

` = sqrt((1 - (9/41)^2)) `

= `sqrt((1 - 81/1681))`

= `sqrt(((1681 - 81)/1681))`
` = 40/41`

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