Question

solve this question ​

Answer 1

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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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