(1+sec2A)(1+sec4A)(1+sec8A)=Tan8A.CotA proveSin6.Sin42.Sin66.Sin78=1/16
jason dhakal , 6 Years ago
Grade 10
Trigonometry> (1+sec2A)(1+sec4A)(1+sec8A)=Tan8A.CotA pr...
1 Answers
Arun
Last Activity: 6 Years ago
Dear student
Please ask one question only in one thread.
We use the trigonometric rules :
2 Sin A Sin B = Cos (A-B) - Cos (A+B)
2 Cos A Cos B = Cos (A-B) + Cos (A+B)
Sin 42° Sin 78° = 1/2 * [ Cos (42° - 78°) - Cos (78° + 42°) ]
= 1/2 * [ Cos 36° - Cos 120°]
= 1/2 [ Cos 36° + 1/2 ]
Sin 6° Sin 66° = 1/2 * [ Cos (6-66) - Cos (6+66) ]
= 1/2 [ Cos 60° - Cos 72° ]
= 1/2 [ 1/2 - Cos 72° ]
Hence, Sin 6° Sin 66° Sin 42° Sin 78°
= 1/16 [ 2 Cos 36° + 1 ] [ 1 - 2 Cos 72° ]
= 1/16 [ 2 Cos 36° - 2 cos 72° + 1 - 4 Cos 36° Cos 72° ]
= 1/16 + 1/8 [ Cos 36° - Cos 72° - 2 Cos 36° Cos 72° ]
= 1/16 + 1/8 [ Cos 36° - Cos 72° - ( Cos (36+72) + Cos (72-36) ) ]
= 1/16 - 1/8 [ Cos 72° + Cos 108° ]
= 1/16 - 1/8 [ Cos 72° - Cos (180° - 108°) ]
= 1/16 - 1/8 [ Cos 72° - Cos 72° ]
= 1/16
Hence Proved.
Regards
Arun (askIITians forum expert)
Provide a better Answer & Earn Cool Goodies
Enter text here...
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
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
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.
Trigonometry
1 Answer Available
Last Activity: 2 Year ago(s)
\tFind the general solution of equation tan3∂=cot2∂For all angles between -720 and +720
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)