Question

If sec there + tan theta= p then find the value of cos ec theta

Answer 1

Hey !!

Sec¢ + tan¢ = p ------1)

1/sec¢ + tan¢ ×sec¢ -tan¢/sec¢-tan¢
[Multiplying by sec¢ -tan¢ on numerator and denominator]

Sec¢ - tan¢ /sec²¢ - tan²¢ = 1/p

Sec¢ - tan¢ = 1/p ----------2)

Adding both equation. 1 and 2

We get

Sec¢ + tan¢ + sec¢ - tan¢ = p +1 /p

2sec¢ = p² + 1/p

2Sec¢ = p² + 1 /p----------3)

Now substracting the equation 2 from 1

We get
Sec¢ + tan¢ -(sec¢ - tan¢ ) = p - 1/p

2tan¢ = p² - 1 /p -------4)

Now dividing the equation 4 to 3 we get

2tan¢ /2sec¢ = p² -1 /p /p² + 1 /p

Sin¢/cos¢ ×cos¢ = p² - 1 /p² + 1

Sin¢ = p² - 1 /p² + 1

1/sin¢ = p² + 1 /p² - 1

Cosec¢ = p² + 1 /p² - 1 Answer

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Hope it helps you !!!

@Rajukumar111