Question

if sec theta + tan theta is equal to K then prove that sin theta equal to K square - 1 / K square + 1​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given : sectheta + tantheta=k

secθ +  tanθ = k

To Find : prove that sin θ=(k²-1)​/(k²+1)

Solution:

secθ + tanθ = k

As we know that

sec²θ - tan²θ =1

=> (secθ +  tanθ )(secθ - tanθ ) = 1

=> (secθ -  tanθ )(k ) = 1

=> secθ - tanθ = 1/k

secθ+ tanθ = k

secθ -  tanθ = 1/k

=> 2secθ = k + 1/k

=>  secθ = (k² + 1)/2k

=> cosθ = 2k/ (k² + 1)

2tanθ = k - 1/k  

=> tanθ  = (  k² - 1 )/2k

sin θ= (k²-1)​/(k²+1)

LHS =  sin θ

=  cosθtan θ

=    (2k/ (k² + 1)) ((  k ²-1  )/2k)

=  (k²-1)​/(k²+1)

= RHS

QED

Hence proved

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