In a right-angled triangle

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

Problem

In a right-angled triangle △ABC\triangle ABC, right angled at CC, the measure of the acute angle AA satisfies sin⁡A=35\sin A = \dfrac{3}{5}. Use this information to answer the following. (i) Find the values of cos⁡(90∘−A)\cos(90^{\circ}-A) and sec⁡(90∘−A)\sec(90^{\circ}-A). (ii) Evaluate P=sin⁡A+cos⁡(90∘−A)+tan⁡(90∘−A)P = \sin A + \cos(90^{\circ}-A) + \tan(90^{\circ}-A) and give your answer as a rational number. (iii) Using the same angle AA, compute Q=sin⁡A csc⁡(90∘−A)+cos⁡A sec⁡(90∘−A)Q = \sin A\,\csc(90^{\circ}-A) + \cos A\,\sec(90^{\circ}-A) and express your answer in simplest form.

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