Question

if theta is an acute angle and 4 sin theta=3, then the value of 4 sin^2 theta - 3 cos^2 theta + 2 is​

Answer 1

Answer:

43/16

Step-by-step explanation:

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Answer 2

Given :

If theta is an acute angle and 4 sin theta=3

To find :

the value of 4 sin^2 theta - 3 cos^2 theta + 2

Solution :

We have

$4 sin theta=3\\sin theta= 3/4$

So rewrite the above expression as

$4 sin^{2} theta - 3 cos^{2} theta +2\\4 sin^{2} theta - 3 (1-sin^{2}) theta +2$

Now substitute all value we get

$4*(3/4)*(3/4)-3(1-(3/4)(3/4))+2\\(9/4)-3(1-(9/16))+2\\(9/4)-3(7/16)+2\\(9/4)-(21/16)+2\\(32-21/16)+2\\(11/16)+2\\(11+32)/16\\43/16$

Hence we get

$4sin^{2} theta - 3 cos^{2} theta +2=43/16$