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Question

tan75°-cot75°=


A

23

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B

2+3

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C

2-3

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D

None of these

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Solution

The correct option is A

23


Explanation for correct option :

Step-1 : Simplifying the above expression

Given expression is : tan75°-cot75°

Applying trigonometric identities : tanA=sinAcosA and cotA=cosAsinA, we get :

tan75°-cot75°=sin75°cos75°-cos75°sin75°=sin275°-cos275°cos75°sin75°

Step-2 : Finding the value of sin275°-cos275°applying the trigonometric identity cos2A=cos2A-sin2A

We have,

sin275°-cos275°=-cos275°-sin275°

=-cos2×75°=-cos150°=-cos180°-30°cos180°-θ=-cosθ=cos30°=32

Step-3 : Finding the value of cos75°sin75° applying the trigonometric identity sin2A=2sinAcosA

We have,

cos75°sin75°=122sin75°cos75°

=12sin150°=12sin180°-30°=12sin30°sin180°-θ=sinθ=12×12=14

Step-4 : Calculating the value of tan75°-cot75°

Using the values obtained in Step-2 and Step-3, we get the value of tan75°-cot75° as follows :

tan75°-cot75°=sin275°-cos275°cos75°sin75°

Putting the obtained values, we have

=3214=23

Hence, the correct answer is option (A).


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