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If cosec x - secx = √5 then find cosecx + secx |
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Answer» GIVEN : cosec x - secx = √5 To find : cosecx + secx Solution: cosec x - secx = √5 Let SAY cosecx + secx = y Adding both 2Cosecx = √5 + y => 2/Sinx = √5 + y => Sinx = 2/(y + √5) 2Secx = y - √5 => 2/Cosx = y - √5 => Cosx = 2/(y - √5) Sin²x + Cos²x = 1 => (2/(y + √5))² + (2/(y - √5))² = 1 => 4((y - √5)² + (y + √5)² ) = (y - √5)² (y + √5)² => 4 ( y² + 5 -2√5y + y² + 5 + 2√5y) = (y² - 5)² => 8( y² + 5) = (y² - 5)² => y⁴ -18y² - 15 = 0 => y² = (18 ± √(-18)² - 4(1)(-15) )/2 => y² = (18 ± 8√6) )/2 => y² = 9 ± 4√6 => y² = 9 + 4√6 ( as Square can not be - ve) => y = √( 9 + 4√6 ) => y = 4.3357 cosecx + secx = √( 9 + 4√6 ) = 4.3357 x = 17.718° Learn more: 2 cosec 2X + cosecx =secx cot (x/2) - Brainly.in show that sin / cosec -1 + cos / 1+sec = sin cos /sin - cos |
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