Sin a cos a(tan a+cot a)
do you want to simplify?
sinacosa(sina/cosa+cosa/sina)
sinacosa[(sina)^2+(cosa)^2]/sinacosa
(sina)^2+(cosa)^2.........
sinacosa(sina/cosa + cosa/sin)
= sin^2 a + cos^2 a
= 1
To simplify the expression sin(a) cos(a) (tan(a) + cot(a), we can break it down step by step:
1. Start with the expression sin(a) cos(a) (tan(a) + cot(a)).
2. Apply the double-angle formula for sine:
sin(2a) = 2sin(a)cos(a).
Now our expression becomes:
sin(2a) (tan(a) + cot(a)).
3. Apply the trigonometric identity for cotangent:
cot(a) = 1/tan(a).
Now our expression becomes:
sin(2a) (tan(a) + 1/tan(a)).
4. Simplify the expression inside the parentheses by finding a common denominator for the terms:
sin(2a) (tan^2(a)/tan(a) + 1/tan(a)).
5. Combine the terms inside the parentheses:
sin(2a) ((tan^2(a) + 1)/tan(a)).
6. Use another trigonometric identity:
tan^2(a) + 1 = sec^2(a).
Now our expression becomes:
sin(2a) (sec^2(a)/tan(a)).
7. Use the identity tan(a) = sin(a)/cos(a):
sin(2a) (sec^2(a)/(sin(a)/cos(a))).
8. Simplify by multiplying the expression by (cos(a)/cos(a)):
sin(2a) (sec^2(a)(cos(a))/(sin(a))).
9. Expand the expression:
sin(2a) ((1/cos^2(a))(cos(a))/(sin(a)).
10. Simplify the expression:
sin(2a)(1/cos(a)).
11. Use the identity sin(2a) = 2sin(a)cos(a):
2sin(a)cos(a)(1/cos(a)).
12. Cancel out the common factor cos(a):
2sin(a).
Therefore, the simplified expression is 2sin(a).