Padhona

Mathematics · Introduction to Trigonometry · NCERT Examples

Example 9

A complete, independently verified solution for NCERT Example 9.

Mathematics · Chapter 8 · NCERT Examples

Download PDF
Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

Example 9

trigonometric identities · in terms of sin

Express cos A, tan A and sec A in terms of sin A.

Solution

Board-exam working:

sin⁡2A+cos⁡2A=1\sin^2A+\cos^2A=1
cos⁡2A=1−sin⁡2A\cos^2A=1-\sin^2A

Since A is acute, cos A is positive.

cos⁡A=1−sin⁡2A\cos A=\sqrt{1-\sin^2A}
tan⁡A=sin⁡Acos⁡A=sin⁡A1−sin⁡2A\tan A=\frac{\sin A}{\cos A}=\frac{\sin A}{\sqrt{1-\sin^2A}}
sec⁡A=1cos⁡A=11−sin⁡2A\sec A=\frac1{\cos A}=\frac1{\sqrt{1-\sin^2A}}

Final answer

cos⁡A=1−sin⁡2A,tan⁡A=sin⁡A1−sin⁡2A,sec⁡A=11−sin⁡2A\cos A=\sqrt{1-\sin^2A},\quad \tan A=\frac{\sin A}{\sqrt{1-\sin^2A}},\quad \sec A=\frac1{\sqrt{1-\sin^2A}}