Consider an isosceles triangle ABC, where AB=AC=1, M is the midpoint of BC, and <BAM=<CAM=x. Use trigonometry to find an expression for BM and by finding BC^2, show that cos2x = 1 - 2(sinx)^2.

Consider the right-angled triangle BAM. We have the hypotenuse and an angle, and want to find the opposite side. Therefore, using SOHCAHTOA, sinx = BM/1, hence BM = sinx. Because M is the midpoint of BC, BC = 2BM = 2sinx. Hence, BC2 = 4(sinx)2Looking at triangle ABC, we have an expression for all sides (AB=AC=1, BC=2sinx) and we have the angle at A (2x). Therefore, we can use the cosine rule to find an expression for BC2.a2 = b2 + c2 - 2bc(cosA).BC2 = 4(sinx)2 = 12 + 12 - 2(1)(1)(cos2x)4(sinx)2 = 2 - 2cos2x2(sinx)2 = 1 - cos2xcos2x = 1 - 2(sinx)2

BS
Answered by Blessie S. Maths tutor

5630 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equation: 2x + y = 7 and 3x - y = 8


25= x2 + 10 - 6. Find X


Which of the following lines is not perpendicular to y=2x+1? (A) y+1/2x=6 (B) 2y=4-x (C) 2x+y=4 (D) y=-1/2(7+x)


If I have £730 in my bank account which has 2.5% compound interest per year, how much more money will be in there after two years?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences