value of (cos A +cosB/sinA-sinB)^2015 +(sinA+sinB/cosA-cosB)^2015=?
Answers
Given: The trigonometric term
(cos A + cosB / sinA - sinB)^2015 +(sinA + sinB / cosA - cosB)^2015
To find: The value of the given expression?
Solution:
- Now we have given the term as:
(cos A + cosB / sinA - sinB)^2015 +(sinA + sinB / cosA - cosB)^2015
- Now we know the formulas :
cos A + cosB = 2 cos(a+b/2) cos (a-b/2)
sinA - sinB = 2 cos(a+b/2) sin(a-b/2)
sinA + sinB = 2 sin(a+b/2) cos(a-b/2)
cosA - cosB = -2 sin(a+b/2) sin(a-b/2)
- Consider first term:
(cos A + cosB / sinA - sinB)^2015
- So putting the values in the expression, we get:
(2 cos(a+b/2) cos (a-b/2))^2015 / (2 cos(a+b/2) sin(a-b/2))^2015
- Cancelling common terms, we get:
(cos (a-b/2))^2015 / (sin(a-b/2))^2015
(cot (a-b/2))^2015
- Consider second term:
(sinA + sinB / cosA - cosB)^2015
- So putting the values in the expression, we get:
(2 sin(a+b/2) cos(a-b/2))^2015 / (-2 sin(a+b/2) sin(a-b/2))^2015
- Cancelling common terms, we get:
(cos (a-b/2))^2015 / (sin(a-b/2))^2015
(cot (a-b/2))^2015
- Not taking them together, we get:
(cot (a-b/2))^2015 - (cot (a-b/2))^2015
0
Answer:
So the answer of the given expression is 0.