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sin + cos = √3
squaring on both side.
(sin + cos )² = (√3)²
sin² + cos² + 2sin.cos = 3 [ (a+b)² = a²+b²+2ab]
1 + 2sin.cos = 3 [ sin²+cos²= 1]
2sin.cos = 3-1
2sin.cos = 2
sin.cos = 1 [ divide by 2 on both sides ]...(1)
According to the question ( प्रश्न के अनुसार )
L.H.S. = tan + cot
= sin / cos + cos / sin
= (sin × sin + cos × cos ) / sin.cos
= ( sin² + cos² ) / sin.cos
= 1 / sin.cos [ sin² + cos² = 1 ]
= 1 / 1 ......from (1)
= 1
= R.H.S.
L.H.S. = R.H.S.
Hence, tan + cot = 1
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