If sin28 equals a and cos 32equals b  calculate b(square root of) 1-a(squared)minus a(square root of) 1-b(squared

1 Answer

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to evaluate `bsqrt(1-a^2)-asqrt(1-b^2)` using the information provides by the problem that `a = sin 28^o` and `b = cos 32^o` , such that:

`cos 32^o*sqrt(1 - sin^2 28^o) - sin 28^o*sqrt(1 - cos^2 32^o)`

Using the Pyhtagorean identities `1 - sin^2 28^o = cos^2 28^o` and `1 - cos^2 32^o = sin^2 32^o` yields:

`cos 32^o*sqrt(cos^2 28^o) - sin 28^o*sqrt(sin^2 32^o)`

Taking the square roots yields:

`cos 32^o*cos 28^o - sin 28^o*sin 32^o`

Using the trigonometric identity `cos alpha*cos beta - sin alpha*sin beta = cos(alpha + beta)` yields:

`cos 32^o*cos 28^o - sin 28^o*sin 32^o = cos (32^o + 28^o)`

`cos 32^o*cos 28^o - sin 28^o*sin 32^o = cos 60^o = 1/2`

Hence, evaluating the given expression, under the given conditions, yields `bsqrt(1-a^2)-asqrt(1-b^2) = 1/2` .