Practicing Success
The value of (1 + cot A − cosec A)(1 + tan A + sec A) − 1 is: |
1 2 3 0 |
1 |
(1 + cot A − cosec A)(1 + tan A + sec A) − 1 = ( 1 + \(\frac{cosA}{sinA}\) - \(\frac{1}{sinA}\) ) . ( 1 + \(\frac{sinA}{cosA}\) + \(\frac{1}{cosA}\) ) - 1 = ( \(\frac{ sinA + cosA - 1 }{sinA}\) ) . ( \(\frac{sinA + cosA +1}{cosA}\) ) - 1 = ( \(\frac{ (sinA + cosA)² - 1² }{sinA . cosA}\) ) - 1 = ( \(\frac{ sin²A + cos²A + 2sinA.cosA - 1}{sinA . cosA}\) ) - 1 { using , sin²A + cos²A = 1 } = ( \(\frac{ 1 + 2sinA.cosA - 1}{sinA . cosA}\) ) - 1 = ( \(\frac{ 2sinA.cosA }{sinA . cosA}\) ) - 1 = 2 - 1 = 1 |