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If sinx + cosx = √2cosx, what will be the value of sinx - cosx ?1. + √2secx2. + √2sinx3. + √2tanx4. + √2cotx |
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Answer» Correct Answer - Option 2 : + √2sinx Given: sinx + cosx = √2cosx Concept Used: sin2x + cos2x = 1 Calculation: sinx + cosx = √2cosx Squaring the equation on both side, we get ⇒ sin2x + cos2x +2sinxcosx = 2cos2x ⇒ 1 + 2sinxcosx = 2cos2x ----(i) Let sinx - cosx = k ----(ii) Squaring the equation on both side, we get ⇒ 1 - 2sinxcosx = k2 Adding (i) and (ii), we get 2cos2x + k2 = 2 ⇒ k2 = 2(1 - cos2x) ⇒ k2 = 2sin2x ⇒ k = +√2sinx ∴ The value of sinx - cosx = +√2sinx |
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