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Find the value of tan45° + cot 30° |
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Answer» -step explanation:GIVEN : Expression \tan^245+\cot^230tan 2 45+cot 2 30To find : The value of the expression ?SOLUTION :Expression \tan^245+\cot^230tan 2 45+cot 2 30We KNOW the trigonometric values,\tan45=1tan45=1 and \cot 30=\sqrt{3}cot30= 3 Substitute,\tan^245+\cot^230=(\tan 30)^2+(\cot 45)^2tan 2 45+cot 2 30=(tan30) 2 +(COT45) 2 \tan^245+\cot^230=(1)^2+(\SQRT3)^2tan 2 45+cot 2 30=(1) 2 +( 3 ) 2 \tan^245+\cot^230=1+3tan 2 45+cot 2 30=1+3\tan^245+\cot^230=4tan 2 45+cot 2 30=4Therefore, the value of the expression is \tan^245+\cot^230=4tan 2 45+cot 2 30=4 |
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