Question

Find the value of:- tan60°/sin60°+cos60°​

Answer 1

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Find the value of:- tan60°/sin60°+cos60°

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Here,

tan60/sin60 + cos60

=> (√3)/(√3/2+1/2)

As we know that tan60 = √3, sin60 = √3/2 & cos60 = 1/2.

=> (√3)/(√3+1)/2

=>2√3/√3+1

On rationalization.

=> (2√3/√3+1).(√3-1/√3-1)

=> (2√3)(√3-1)/(√3+1)(√3-1)

=> (6-2√3)/(√3²-1²)

Because a²-b² = (a+b)(a-b)

=> (6-2√3)/2

=>3-√3 <<<<<Ans.

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Answer 2

Answer:

Here,

tan60/sin60 + cos60

=> (√3)/(√3/2+1/2)

As we know that tan60 = √3, sin60 = √3/2 & cos60 = 1/2.

=> (√3)/(√3+1)/2

=>2√3/√3+1

On rationalization.

=> (2√3/√3+1).(√3-1/√3-1)

=> (2√3)(√3-1)/(√3+1)(√3-1)

=> (6-2√3)/(√3²-1²)

Because a²-b² = (a+b)(a-b)

=> (6-2√3)/2

=>3-√3 <<<<<Ans.

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