Question

If sec theta + tan theta = p
then find the value of cosec theta​

Answer 1

Answer:

Refer to the attachment for ur answer...

Answer 2

Hi !

Solution :-

• Method :-01

Given :- Sec¢ + tan¢ = P ________(1)

By rationalisation process .

1/sec¢+tan¢ = 1/p

dividing and multiplying by sec¢ - tan¢

We get ,

sec¢ - tan¢ /sec²¢-tan²¢ = 1/p

but as we know that , sec²¢ - tan²¢ = 1

•°• sec¢ - tan¢ = 1/p _________(2)

adding both equation .

we get , 2sec¢ = p + 1/p

sec¢ = p²+1/2p

sec¢ = p/h= p²+1/2p

cos¢ = 2p/p²+1 , {sec¢ = 1/cos¢}

sin²¢ = 1- cos²¢

sin²¢ = 1 -(2p/p²+1)²

sin²¢ = 1- 4p² /p⁴+1+2p²

sin²¢ = p⁴ + 1+2p²-4p²/p⁴+1+2p²

sin²¢ = p⁴+1-2p²/(p²+1)²

sin²¢ = (p²-1)²/(p²+1)²

sin¢ = p²-1/p²+1

as we know that ,sin¢ = 1/cosec¢

since, cosec¢ = p²+1/p²-1 Answer

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• Method :-02

Sec¢ + tan¢ =p

1/cos¢ + sin¢ /cos¢ = p

1+sin¢ /cos¢ = p

Squaring both sides .

(1+sin¢)²/cos²¢ = p²

(1+sin¢)(1+sin¢)/(1-sin²¢) = p²

(1+sin¢)/(1-sin¢) = p²

1+sin¢ = p²-p²sin¢

sin¢ + p²sin¢ = p²-1

sin¢ (1+p²) = p²-1

sin¢ = p²-1/p²+1

Now, cosec¢ = 1/sin¢ (we already know )

so, cosec¢ =p²+1/p²-1 Answer

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Hope it's helpful