If dθ cos^2 ⁡ ( tan ⁡2 + sec ⁡2 )= tan ⁡ +2 log_e ⁡ |f ( ) |+C where cis a constant of integration,then the ordered pair ( ,f ( ) )is equal to:

Question

Accepted Answer

Correct answer: C. (c) sec^2 1+ tan^2 ⁡ 1- tan^2 ⁡ + 2 tan ⁡ 1- tan^2 ⁡ dθ = sec^2 ⁡ (1- tan^2 ⁡ ) (1+ tan ⁡ )^2 dθ = sec^2 ⁡ (1- tan ⁡ )1+ tan ⁡ dθ tan ⁡ =t ⇒ sec^2 ⁡ θdθ= dt = ( 1-t1+t ) dt= (-1+ 21+t) dt =-t+2 log ⁡ (1+t )+C =- tan ⁡ +2 log ⁡ (1+ tan ⁡ )+C ⇒ =-1 and f ( )=1+ tan ⁡

$If \int \frac{dθ}{cos ^{2} θ ( tan 2 θ + sec 2 θ )} = λ tan θ + 2 log_{e} | f (θ) | + C where c is a constant of integration,then the ordered pair (λ, f (θ)) is equal to:$

Solution

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