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

6550 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The cubic polynomial f(x) is defined by f(x) = 2x^3 -7x^2 +2x+3. Express f(x) in a fully factorised form.


Where z is a complex number, what is the cartesian form of |Z-2+3i| = 1?


What is the difference between a definite integral and an indefinite integral?


The normal to the curve C when x=1 intersects the curve at point P. If C is given by f(x)=2x^2+5x-3, find the coordinates of P


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences