0

Guest

Courses New

cos A=m cos B, then prove that cot (A+B/2)=( m+1/m-1)tan(B-A/2)

cos A=m cos B, then prove that cot (A+B/2)=( m+1/m-1)tan(B-A/2)

Grade:10

1 Answers

Vikas TU
14149 Points
7 years ago

Sol:

Given Cos A = m Cos B

⇒ Cos A / Cos B  = m / 1. ( apply componendo and dividendo)

⇒ (Cos A + Cos B) / (Cos A - Cos B)  = ( m + 1) / (m - 1)

⇒ {(2 Cos ( A+B) / 2 × Cos (A-B) / 2 } / {(- 2 Sin ( A+B) / 2 × Sin (A-B) / 2 }  = ( m + 1) / (m - 1)

⇒ {(2 Cos ( A+B) / 2 × Cos (B - A) / 2 } / {( 2 Sin ( A+B) / 2 × Sin (B - A) / 2 }  = ( m + 1) / (m - 1)

⇒ {( Cot ( A+B) / 2 × Cot (B - A) / 2 } = ( m + 1) / (m - 1)

⇒ {( Cot ( A+B) / 2 = { ( m + 1) / (m - 1) } Tan (B - A) / 2

Here x = ( m + 1) / (m - 1).

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More