Let be an acute angle such that .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let

B

be an acute angle such that

\cos B = \dfrac{4}{5}

. (i) Find the numerical values of

\sin B

and

\tan B

. (Give each answer in simplest fractional form.) (ii) Using the values obtained in part (i), determine the value of

P = \frac{\tan^{2}B + \sec B}{\cot B + \csc^{2}B}.

Write your answer as a rational number.