1.

If sinx + cosx = √2cosx, what will be the value of sinx - cosx ?1. + √2secx2. + √2sinx3. + √2tanx4. + √2cotx

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



Discussion

No Comment Found

Related InterviewSolutions