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3 tan 25° tan 40 tan 50 tan 65 an 604 (cos229 cos 619)33. Evaluate: |
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Answer» Numerator = 3 tan 25° tan 40° tan 50° tan 65° - (1/2) tan² 60° = 3 ( tan 25 tan 65 ) ( tan 40 tan 50 ) - (1/2) ( √3 )² = 3 ( tan 25 cot 25 ) ( tan 40 cot 40 ) - (3/2) = 3(1)(1) - (3/2) = 3/2 ......................... (1) Denominator = 4 ( cos² 29° + cos² 61° ) = 4 ( sin² 61° + cos² 61° ) = 4(1) = 4 ..............................(2) From (1) and (2), Required Expression = ( 3/2 )/4 = 3/8 Ans. |
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