Question

prove tan theta + sec theta-1/
tan theta - sec theta +1 = 1+sin
theta/ cos theta = sec theta +
tan theta​

Answer 1

Answer:
Hey Mate,
We have to prove LHS = RHS
LHS = ( tan\theta+sec\theta-1 ) / ( tan\theta-sec\theta+1 )
RHS = (sin\theta+1) / cos\theta
Lets Start from LHS
LHS = ( tan\theta+sec\theta-1 ) / (tan\theta-sec\theta+1 )
= ( tan\theta+sec\theta-(sec^{2}\theta-tan^2\theta )) / ( tan\theta-sec\theta+1 )
= (tan\theta+sec\theta-[(sec\theta+tan\theta)(sec\theta-tan\theta)])/(tan\theta-sec\theta+1 )
= (tan\theta+sec\theta[tan\theta-sec\theta+1]) / (tan\theta-sec\theta+1 )
= tan\theta+sec\theta
= [sin\theta/cos\theta] + [1/cos\theta]
= [(sin\theta+1) /cos\theta] = RHS
Hence Proved,
LHS=RHS

Answer 2

we have to prove that LHS=RHS

theta=a

then

(tan a+sec a-1)/(tan a-sec a+1)

(tan a+sec a-(sec^2a-tan^2a))/(tan a-sec a+1)

(tan a+sec a-(sec a+tan a) (seca-tana))/(tan a-sec a+1)

(tan a+sec a-(sec a+tan a)(seca-tana) /(tan a-seca+1)

(tan a+ seca) (1-(seca-tana))/(tan a-sec a+1)

(tan a+ seca)

-------------------

(sin a/cos a) +(1/cos a)

here Lcm is cos a

(sin a+1)/cos a

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