By first proving that sin2θ=2sinθcosθ, calculate ∫1+sinθcosθ dθ.

We have, from the formula book, sin⁡(A±B)=sinAcosB±cosAsinB Using A=B=θ, we have sinθ+θ=sinθcosθ+cosθsinθ Which we can simplify to sin2θ=2sinθcosθ as required. We can then substitute this into the integral: 1+1/2sin2θ dθ From this we can calculate the integral, 1+1/2sin2θ dθ =θ-1/4cos2θ+c where c is an arbitrary constant.

AH
Answered by Abigail H. Maths tutor

6868 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find, using calculus, the x coordinate of the turning point of the curve with equation y=e^3x cos 4


How do I use the chain rule for differentiation?


Use the chain rule to show that, if y = sec(x), then dy/dx = sec(x)tan(x).


Given that y=(4x+1)^3sin 2x , find dy/dx .


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning