Mark (√) against the correct answer of the following: ∫ log tan x sin x cos x dx =? ∫ l o g t a n x s i n x c o s x d x =?
∫ (log tan x)/ (sin x cos x) dx = ? Log |log (tan x )| + c. 1 2 1 2 (log tan x)2 + c.
Log (sin x cos x) + c. Rewrite [math processing error] tan ( x) in terms of sines and cosines. Rewrite [math processing error] sin ( x) cos ( x) sin ( x) as a product.
Cancel the common factor of [math processing error] sin ( x). Tap for more steps. Convert from [math processing error] 1 cos ( x) to [math processing error] sec ( x).
1. tanx = sinx cosx. 2. sin2x + cos2x = 1. 3. secx = 1 cosx.
To verify the given identity, start by working on the left side. Rewrite tanx in terms of sinx and cosx. = sinx cosx ⋅ sinx +cosx.
Tan(x) sin(x)= 1 csc(x) cos(x)= 1 sec(x) tan(x)= 1 cot(x) even/odd identities sin(x)=sin(x) cos(x) = cos(x) tan(x)=tan(x) csc(x)=csc(x) sec(x)=sec(x) cot(x)=cot(x) pythagorean identities cos2(x)+sin2(x)=1 tan2(x)+1=sec2(x) cot2(x)+1=csc2(x) sum identities sin(x+y)=sin(x)cos(y)+cos(x)sin(y) cos(x+y) = cos(x)cos(y)sin(x)sin(y) tan(x+y)= tan(x)+tan(y).
