To find sin of inverse cos x, first we have to convert cos -1 into sin -1. Then sin (cos -1 x) = sin (sin -1 √ (1-x 2 )) = √ (1-x 2 ). Sin of sin inverse of x is x only when x is present in the interval [-1, 1]. In the same way, sin inverse of sin of x is x only when x is present in the interval [-π/2, π/2]. Sin Inverse x Formula. In a right-angled triangle, the sine of an angle (θ) is the ratio of its opposite side to the hypotenuse. i.e., sin θ = (opposite side) / (hypotenuse). Then by the definition of inverse sine, θ = sin -1 [ (opposite side) / (hypotenuse) ] . As the image below shows, to find the measure of the angle θ, we use the sin Join Teachoo Black. Derivative of 〖𝒄𝒐𝒔𝒆𝒄〗^ (−𝟏) 𝒙 𝑓 (𝑥)=〖𝑐𝑜𝑠𝑒𝑐〗^ (−1) 𝑥 Let 𝒚= 〖𝒄𝒐𝒔𝒆𝒄〗^ (−𝟏) 𝒙 cosec⁡〖𝑦=𝑥〗 𝒙=𝐜𝐨𝐬𝐞𝐜⁡〖𝒚 〗 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑥/𝑑𝑥 = (𝑑 (cosec⁡𝑦 ))/𝑑𝑥 1 Answer link. sin (cos^-1 x) =sin (sin^-1sqrt (1-x^2))=sqrt (1-x^2) (proved) Let cos^-1x=theta :. cos theta= x . We know cos theta=a/h =x/1 where a (=x),adjacent side in a right angled triangle , and h (=1),is the hypotenuse, then by pythagorus theorm ,opposite side (o). o=sqrt (1-x^2) :.sin theta= o/h=sqrt (1-x^2)/1 :. theta=sin^-1 sqrt (1-x^2 Mathematically, the sin inverse integral is written as ∫arcsin x dx = ∫sin-1 x dx = x sin-1 x + √(1 - x 2) + C. Integral of sin inverse x is also called the antiderivative of sin inverse x. Integration of sin inverse can be done using different methods such as integration by parts and substitution method followed by integration by parts. rQbxnm.

sin 1x cos 1x formula