Question

Given sin theta=3/4 and π/2 is smaller than equal to theta smaller than equal to π. Find the value of a. sin 2q b. cos 2q c sec 2theta?

Answer 1

Please see below.

Explanation:

I think this is your first question.

So there may be some typing mistake.

I tried for following question.

Question:`If, sintheta=3/4, andpi/2 <= theta <=pi`, then find

`(a)sin2q tosin2theta,(b)cos2qto cos2theta and (c)sec2theta`

Now,

#sintheta=3/4,and pi/2 <= theta <= pi=>color(pink)(II^(nd) Quadrant=>costheta <0#

`:.costheta=-sqrt(1-sin^2theta)=-sqrt(1-9/16)=-sqrt7/4`

So,

#color(red)((a)sin2theta=2sinthetacostheta=cancel2(3/cancel4_2)(-sqrt7/4)=- (3sqrt7)/8#

`color(blue)((b)cos2theta=cos^2theta-sin^2theta`

`cos2theta=(-sqrt7/4)^2-(3/4)^2=7/16-9/16=-2/16=-1/8`

`color(violet)((c)sec2theta=1/(cos2theta))=1/(-1/8)=-8`
Note:
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