Q. 17

# Prove that <span

To prove:

Explanation:

LHS = cot θ - tan θ

But we know ,

substituting these values in LHS, we get

But we know cos2θ + sin2θ = 1

sin2θ = 1 - cos2θ, substituting this value in above equation, we get

= RHS

Hence proved

OR

To prove sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ

Proof: LHS = sin θ (1 + tan θ) + cos θ (1 + cot θ)

But we know,

,

substituting these values in LHS, we get

Now taking cos θ + sin θ common, we get

But we know cos2θ + sin2θ = 1,

substituting this value in above equation, we get

Cancelling the like terms, we get

But we know ,

substituting these values in above equation, we get

= cosec θ + sec θ

= RHS

Hence proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses