0

Guest

Courses New

If sin x + cos x =√2cos x then prove that cos x - sin x = √2 sin x

If sin x + cos x =√2cos x then prove that cos x - sin x = √2 sin x

Grade:11

3 Answers

Kshitij K
44 Points
5 years ago
sinx+cosx=21/2cosx
=> sinx=(21/2-1)cosx
=> tanx=(21/2-1).
For Other:-
We’ve to prove cosx-sinx=21/2sinx.
OR We can prove this:- cosx=(21/2+1)sinx
OR We can prove this:- cotx=(21/2+1).
ORIGINALLY we had proved:- tanx=(21/2-1)
=> cotx=1/(21/2-1)
On Rationalising we get:
cotx=(21/2+1), which is the required proof.
 
Shruti Singh
13 Points
4 years ago
Cos x + sin x = √2 cos xSin x = (√2-1)cos xMultiplying both sides with (√2+1), we get(√2+1)sin x = (√2+1)(√2-1)cos x√2 sin x + sin x = cos xCos x - sin x = √2 sin x
Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the answer to your question.
 
cos x + sin x = √2 cos x
Sin x = (√2-1)cos x
Multiplying both sides with (√2+1),we get
(√2+1)sin x = (√2+1)(√2-1)cos x
√2 sin x + sin x = cos x
cos x - sin x = √2 sin x
 
Thanks and regards,
Kushagra
 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

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