Question

Find the value of cot105°

Answer 1

Hey !!!

cot105° = cot ( 90° + 15°)

-tan15° = -sin²15° /cos15°

sin15° = √3 - 1/2√2

cos15° = √3 + 1 /2√2

hence, - tan15° = -(√3 - 1 /)√3 + 1

simply rationalising

-(1 -√3 ) / ( √3 + 1 ) × ( √3 - 1)/ ( √3 - 1)

=> - ( 1 + 3 - 2√3) / ( 3 - 1)

=> -2( 2 - √3)/2 = √3 - 2 Answer ✔

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Hope it helps you !!!

@Rajukumar111