An acute angle satisfies .

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

An acute angle

\theta

satisfies

\sin \theta - \cos \theta = \dfrac{1}{3}

. (i) Prove that

\sin \theta + \cos \theta = \dfrac{\sqrt{17}}{3}

. (ii) Hence determine the exact values of

\sin \theta

and

\cos \theta

. (iii) Obtain the value of

\tan \theta

and verify that

\sin^{2}\!\theta + \cos^{2}\!\theta = 1

for the values found.