Question

If cos A =1/2 and sin B =1/√2 , find the value of tan A - tan B /1 + tanAtanB

Answer 1

the final answers is 1

Answer 2

HEY FRIEND

HERE IS YOUR ANSWER

GIVEN :
_____

cosA=1/2

cos60°=1/2

So, A=60°

sinB=1/√2

sin45°=1/√2

So, B=45°

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WE GET

A=60°
B=45°

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=(tanA-tanB) / (1+tanAtanB)

=(tan60°-tan45°)/(1+tan60°tan45°)

[PUTTING tan60°=√3 and tan45°=1]

=(√3-1) / (1+√3×1)

=(√3-1) / (√3+1)

WE CAN ALSO RATIONALISE IT

=(√3-1)×(√3-1) / (√3+1)×(√3-1)

[USING (a-b)²=a²+b²-2ab and (a+b)(a-b)=a²-b²]

=[(√3)²+(1)²-2×1×√3] / (√3)²-(1)²

=(3+1+2√3) / (3-1)

=(4+2√3)/2

=2(2+√3)/2

=2+√3

HOPE THIS HELPS YOU ☺