Question

if sec theta- tan theta ==4,then prove that costheta=8/17​

Answer 1

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Answer 2

Answer:

PROOVED BELOW

Step-by-step explanation:

1/cos theta=sec theta

sin theta/cos theta=tan theta

Now solving Lhs,we get:

1/cos theta-sin theta/cos theta=4

1-sin theta/cos theta=4.......(A)

we know that sec^2 theta-tan^2 theta=1

sec theta-tan theta×sec theta+tan theta=1

sec theta +tan theta=1/sec theta -tan theta

B.sec theta + tan theta=1/4(from (A))

dividing A and B

1+sin theta/1-sin theta =1/4/4

1+sin theta/1-sin theta=1/16

16+16sin theta =1-sin theta

17 sin theta=-15

sin theta =-15/17

sin^2 theta=225/ 289

cos^2theta =1-sin^2 theta =1-225/289

cos^2theta= 64/289

cos theta=√64/289

cos theta=8/17