Question

Proving trig equations
\(\bf (sin~x)(tan~x~cos~x~-~cot~x~cos~x)~=~1~-~2~cos^2x\\\)

Answer 1

@ganeshie8

Answer 2

@SolomonZelman

Answer 3

Start off by writing cotangent and tangent in sine and cosine terms

Answer 4

focusing on the left side first

Answer 5

sin(x)*tan(x)*cos(x) = sin(x)*sin(x)/cos(x)*sin(X) = sin(x)*sin(x)=sin^2(x)
sinx *cot(x) *cos(x) = sin(x)*cos(x)/sin(x)*cos(x) = cos(x)*cos(X) =cos^2(x)

Answer 6

Mhm

Answer 7

tan=sin/cos
cot=cos/sin

Answer 8

I think we can verify it

Answer 9

Yes I have to verify it and prove that it is true

Answer 10

1= sin^2(x) + cos^(x)
sin^2(x) = 1- cos^(x)
1- cos^2(x) -cos^2(x) = 1- 2*cos^2(x) this answer

Answer 11

\[sinx(\frac{ sinx }{ cosx }cosx-\frac{ cosx }{ sinx }cosx)=1-2\cos^2x\]

Answer 12

Yeah borak got it

Answer 13

Ok, thank you all for the help