Prove that: [sqrt{frac{1 – sintheta}{1 + sintheta}} = sectheta – tantheta]
Chapter 6 – Trigonometry – Text Book Solution
Practice Set 6.1| Q 6.3 | Page 132
Prove that:
[sqrt{frac{1 – sintheta}{1 + sintheta}} = sectheta – tantheta]
[sectheta = frac{1}{costheta}]
[tantheta = frac{sintheta}{costheta}]
[sin^2theta + cos^2theta = 1]
[frac{1}{cos^2theta} = tan^2theta + 1]
Starting with the left-hand side:
[sqrt{frac{1 – sintheta}{1 + sintheta}}]
[= sqrt{frac{(1 – sintheta)^2}{(1 – sin^2theta)}}]
[= sqrt{frac{(1 – sintheta)^2}{cos^2theta}}]
[= frac{1 – sintheta}{costheta}]
Now we can substitute the identity for
[costheta:]
[= frac{1 – sintheta}{frac{1}{sectheta}}]
[= sectheta(1 – sintheta)]
[= sectheta – secthetasintheta]
[= sectheta – frac{sintheta}{costheta}]
[= sectheta – tantheta]
Therefore, we have shown that
[ sqrt{frac{1 – sintheta}{1 + sintheta}} = sectheta – tantheta.]
Solution
Chapter 6 – Trigonometry – Text Book Solution
Practice set 6.1 |Q 6.3 | P 131
Click Here to see All the Textbook solution of Geometric Construction