If sinx + cosx = √2cosx, what will be the value of sinx – cosx ?
1. + √2secx
2. + √2sinx
3. + √2tanx
4. + √2cotx
1. + √2secx
2. + √2sinx
3. + √2tanx
4. + √2cotx
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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