Question

Question 28 If x belongs to the set (0, 1), write cos(sin 1 (4x)) as an algebraic expression in x. Hint... draw a triangle. BI YA - A IX E E71 XX, • 2 Vẽ MT VI 12pt Paragraph

Answer 1

SOLUTION;

THE equation is.

$Cos(sin^{-1}(4x))$ where interval of cos (0,1]

That means this is 1st quadrant where all tangent sin cos is positive

Now,

$Cos(sin^{-1}(4x))=cos\theta$

Where we say that,

$sin^{-1}(4x)=\theta$

$sin\theta=4x$

We know that,

$Cos\theta=\sqrt{1-(sin\theta)^{2}}=\sqrt{1-(4x)^{2}}=\sqrt{1-16x^{2}}$so,

$Cos\theta=\sqrt{1-16x^{2}}$

$Cos\theta=cos(sin^{-1}(4x))=\sqrt{1-16x^{2}}$

Answer

$cos(sin^{-1}(4x))=\sqrt{1-16x^{2}}$