Verify the identity sin x + cos x * cot x = csc x..?
(sin x cot x)/(cos x csc x) = (sin x • cos x/sin x)/(cos x • 1/sin x) = cos x • sin x/cos x = sin x (1 + csc x)(sec x - tan x) = (1 + 1/sin x)(1/cos x - sin x/cos x) = (sin x + 1)/sin x • (1 - sin x)/cos x = (1 - sin^2 x)/(sin x cos x) = cos^2 x/(sin x cos x) = cos x/sin x = cot x
Verify the identity: cscx(cscx-sinx)+(sinx-cosx)/(s...
csc = 1/sin, cot = cos/sin (1/sin x)*((1/sin x) - sin x)+ (1/sin x)*(sin x - cos x) + (cos x/sin x) (1/sin x)*((1/sin x) - sin x)+ (1/sin x)*(sin x - cos x + cos x) (1/sin x)*((1/sin x) - sin x)+ 1 (1/sin^2 x)*(1 - sin^2 x) + (sin^2 x/sin^2 x) (1/sin^2 x)*(1 - sin^2 x + sin^2 x) (1/sin^2 x) cxc^2 x <<<
Prove Identity cscx(cscx - sinx) + sinx - cosx/sinx + cotx = csc^2x?
cscx(cscx - sinx) + sinx - cosx/sinx + cotx = csc²x - cscx.sinx + sinx - cotgx + cotgx = csc²x - (1/sinx).sinx + sinx = 1/sin²x - 1 + sinx = 1 + cotg²x - 1 + sinx = cotg²x + sinx = cos²x/sin²x + sinx = cos²x/sin²x + sin²x.sinx/sin²x = ( cos²x + sin²x )sinx / sin²x = sinx / sin²x = 1 / sinx = cscx ( I think cscx can't csc²x )
Prove the identity. cscx - cotx cosx = sinx?
Prove the identity. cscx - cotx cosx = sinx? Using the left hand side of the identity...begin by using the identities... csc x = 1/sin x and cot x = (cos x)/(sin x) csc x - cot x cos x = (1/sin x) - (cos x/sin x)(cos x) <-- simplify.. = (1/sin x) - (cos^2 (x))/(sin x) <-- since these have common denominators, add tops... = (1 - cos^2 (x))/sin x Now use alternate form of this identity: sin^2 (x) + cos^2 (x) = 1 which is sin^2 (x) = 1 - cos^2 (x) just by subtracting cos^2 (x) both sides.. = (sin^2 (x))/sin x <-- simplify.. = sin x <-- Q.E.D., done!
Verify cotx + (sinx / 1 +cosx) = cscx?
LHS = cot x + sin x(1-cos x)/((1-cos x)(1+cos x)) = cot x + sin x(1-cos x)/ (1- cos ^2 x) = cot x + sin x(1-cos x)/ sin ^2 x = cot x + (1-cos x)/ sin x = cot x + csc x - cot x = csc x proved Note: when we have 1+cos x in denomiator we can multiply (1-cos x) to both numerator and denominator then denominator becomes 1- cos^2x or sin^2 x thus get simplified.
Prove identity ( 1+Tan x+Cot x)( Cos x-Sin x)=( Csc x/Sec x^2) - ( Sec x/Csc x^2)?
Distribute all terms: cos x + cos x tan x + cos x cot x - sin x - sin x tan x - sin x cot x = csc x/sec^2 x - sec x/csc^2 x Use the identities (tan x = sin x/cos x), (cot x = cos x/sin x), (csc x = 1/sin x), (sec x = 1/cos x): cos x + sin x + cos^2 x/sin x - sin x - sin^2 x/cos x - cos x = (1/sin x)(cos^2 x) - (1/cos x)(sin^2 x) Simplify: cos^2 x/sin x - sin^2 x/cos x = cos^2 x/sinx - sin^2 x/cos x
Verify: csc x-sin x=(cot x)(cos x)?
csc x - sin x = 1/sin x - sin x = (1-sin²x)/sin x = cos²x/sinx .......cos x = --------- * cos x = cot x cos x .......sin x
Sin x + cot x cos x = csc x Use the fundamental identities to verify the following identities.?
sin x + cot x cos x = csc xs5n x* sin x + (cos x)(cos x)/(sin x) = csc x sin x + (cos² x)/(sin x) = csc x (sin² x + cos² x)/sin x = csc x but sin² x + cos² x = 1 therefore: 1/(sin x) = csc x csc x = csc x Proven!