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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 23 of 61
Marks: +1, -0
cos (π4−x)\left(\frac{\pi}{4} - x\right) cos (π4−y)\left(\frac{\pi}{4} - y\right) - sin (π4−x)\left(\frac{\pi}{4} - x\right) sin (π4−y)\left(\frac{\pi}{4} - y\right) = sin (x + y)
Solution:  
L.H.S. = cos (π4−x)\left(\frac{\pi}{4} - x\right) cos (π4−y)\left(\frac{\pi}{4} - y\right) - sin (π4−x)\left(\frac{\pi}{4} - x\right) sin (π4−y)\left(\frac{\pi}{4} - y\right)
= cos (π4−x+π4−y)\left(\frac{\pi}{4} - x + \frac{\pi}{4} - y\right) [Since cos (A + B) = cosA cosB – sinA sinB]
= cos (π2−(x+y))\left(\frac{\pi}{2} - (x+y)\right) = sin (x + y) = R.H.S. (Since cos (π/2 - θ) = sin θ)
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