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Give the Answer in Attachment.


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Answer 1

given

cos X/2=3/5

sinx/2=4/5

tanx/2=4/3

i attached solution above wait comments is banned so if wrong tell here

Answer 2

Answer:

Given cos x/2 = - 7/25 .

Also the range of x is given here as :-

180° < x < 270°

This means that x lies in the 3rd quadrant .

So x/2 should lie in the 2nd quadrant .

cos x = - 7/25

We know that cos x/2 = ± √( 1 + cos x )/2

cos x/2 will be negative as x/2 lies in the 2nd quadrant .

⇒ cos x/2 = - √( 1 + cos x )/2

⇒ cos x/2 = - √( 1 - 7/25 )/2

⇒ cos x/2 = - √( 18/25 )/2

⇒ cos x/2 = - √18/50

⇒ cos x/2 = - √9/25

⇒ cos x/2 = - 3/5

sin x/2 will be positive as x/2 is in the 2nd quadrant .

We know that sin x/2 = ± √( 1 - cos x ) /2

⇒ sin x/2 = √( 1 + 7/25 )/2

⇒ sin x/2 = √( 25 + 7 )/25/2

⇒ sin x/2 = √32/50

⇒ sin x/2 = √16/25

⇒ sin x/2 = 4/5

tan x/2 = ( sin x/2 ) / ( cos x/2 )

⇒ tan x/2 = 4/5 / ( -3/5 )

⇒ tan x/2 = - 4/3

Explanation:

There are 4 quadrants in the coordinate system .

Remember the ALL-SIN-TAN-COS Rule .

All ratios are positive in the first quadrant .

The ratio of sine is positive in the second quadrant .

The ratio of tan is positive in the third quadrant .

The ratio of cos is positive in the fourth quadrant .