Question

If 2sec theta+3tan theta=7,then the
value of 2tan theta+3sec theta =?

Answer 1

Solution :

Here I am using A instead of theta.

2secA + 3tanA = 7 --( 1 ) given

Do the square both sides of

the equation , we get

(2secA+3tanA)² = 7²

=> 4sec² + 9tan²A+12secAtanA=49

=> 4(1+tan²A)+9(sec²A-1)

+12secAtanA = 49

[ By trigonometric identity ,

Sec²A - tan² A = 1 ]

=> 4+4tan²A+9sec²A-9

+ 12secAtanA = 49

=> 4tan²A+9sec²A+12tanAsecA

= 49 + 9 - 4

=> (2tanA)² +(3secA)²

+ 2×2tanA× 3secA = 54

=> ( 2tanA + 3secA )² = 54

=>2tanA + 3secA = ± √54

=> 2tanA + 3secA = ± 3√6

••••

Answer 2

Thank you for asking this question. Here is your answer:

First of all we will solve this:

2 sec theta + 3 tan theta will be equal to 7

2(1/cos theta)+3(sin theta/ cos theta) equal to 7

(2 + 3 sin theta)/cos theta equal to 7

2 + 3 sin theta will be equal to 7 cos theta

cos theta will be equal to (2 + 3 sin theta)/7

If there is any confusion please leave a comment below