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Trigonometric function and compound angle. Prove that; Tan5a+​​tan3a/tan5a-tan3a=sin8a/sin2a

Trigonometric function and compound angle. 
Prove that; 
  1. Tan5a+​​tan3a/tan5a-tan3a=sin8a/sin2a

Grade:11

1 Answers

Garvit Garg
25 Points
5 years ago
To solve this equation you have to firstly convert tan in sin and cosin and then by taking LCM and using formula sin(a)cos(b)+cos(a)sin(b)  we can get the answer  i.e.
Tan5a = sin 5a / cos 5a
Tan3a= sin 3a / cos 3a
Putting values in equation and taking LCM we will get
[(sin 5a)(cos 3a) + (cos 5a)(sin 3a)]  / [(sin 5a)(cos 3a) - (cos 5a)(sin 3a)]
Now using formula 
(sina)(cosb) + (cosa)(sinb) = sin(a+b)
(sina)(cosb) - (cosa)(sinb) = sin(a-b)
We will get sin8a/sin2a
 

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