Question

if 7sec²- 3tan²A =11 then show that Sin A =1/2 ​

Answer 1

To prove

If 7 sec²A - 3 tan²A = 11

Then sin A =1/2

Proof

7 sec²A - 3tan²A = 11

We know that

1 + tan²A = sec²A

Putting the value of sec²A

7( 1 + tan²A ) - 3 tan² A = 11

7 + 7 tan²A - 3 tan² A = 11

Taking tan²A common

7+ tan ²A ( 7-3). = 11

7 + 4 tan²A. = 11

4 tan²A. = 11- 7

tan²A. = 4/4 = 1

tan²A. = 1²

As we know that 1² = 1

tan A. = 1

tan A. = tan 45°

( tan45° = 1)

A = 45°

Now , in terms of sin

Sin A = Sin 45°

Sin 45° = 1/2

Hence proved

Answer 2

Refer the attachment.