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If secx + tanx = 3, find cosecx + cotx.1. 32. 13. 04. 2 |
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Answer» Correct Answer - Option 4 : 2 Given: secx + tanx = 3 Concept Used: If secx + tanx = y. then secx - tanx = 1/y cosec2x - cot2x = 1 tanx = 1/cotx Calculation: secx + tanx = 3 ----(i) secx - tanx = 1/3 ----(ii) Subtracting (ii) from (i), we get 2tanx, 2tanx = 8/3 ⇒ tanx = 4/3 ⇒ cotx = 3/4 cosecx = √(1 + cot2x) ⇒ √(1 + 9/16) ⇒ √(25/16) ⇒ 5/4 cosecx + cotx = 5/4 +3/4 ⇒ 2 ∴ The value of cosecx + cotx is 2. |
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