If a+b=c, prove that cos^2 a+cos^2b+cos^2c =1+2cosacosbcosc
If a+b=c, prove that cos^2 a+cos^2b+cos^2c =1+2cosacosbcosc
agam goel , 11 Years ago
Grade 12
Trigonometry> If a+b=c, prove that cos^2 a+cos^2b+cos^2...
1 Answers
Y RAJYALAKSHMI
cos^2a +cos^2b+cos^2c= (1+cos2a)/2+(1+cos2b)/2+cos^2c
=1+(1/2)*(2cos(a+b)cos(a-b) +cos^2c (since a+b+c = 0)
=1 + cos(-c)cos(a-b)+cos^2c (since cos(-a) = cosa)
=1+cos(c)cos(a-b)+cos^2c
=1+cosc(cos(a-b)+cos(a+b) (since a+b+c = 0 & cos(-a) = cosa)
=1+cosc(2cosacosb)
=1+2cosacosbcosc
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available
Last Activity: 3 Years ago
- Find the general solution of equation tan3β=cot2β
For all angles between -720 and +720
- Find the general solution of equation tan3β=cot2β
For all angles between -720 and +720
trigonometry
1 Answer Available
Last Activity: 3 Years ago
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
1 Answer Available
Last Activity: 3 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
1 Answer Available
Last Activity: 3 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? limπ₯β0 π ππ6π₯/5π₯
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? limπ₯β0 π ππ6π₯/5π₯
trigonometry
1 Answer Available
Last Activity: 3 Years ago