if cosA =1/2, sinB =1/ √2 find the valueof tanA -tanB / 1+tanAtanB
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Cos A=1/2
A=60°
Cos B=1/✓2
B=45°
To find:Tan A-tan B/1+tan AtanB
Tan60°-tan45°/1+tan60°tan45°
✓3-1/1+✓3.1
✓3-1/✓3+1
Rationalizing
✓3-1.✓3-1/✓3+1.✓3-1
(✓3-1)^2/(✓3)^2-2
3+1-2✓3/3-1
4-2✓3/2
2(2-✓3)/2
2-✓3
A=60°
Cos B=1/✓2
B=45°
To find:Tan A-tan B/1+tan AtanB
Tan60°-tan45°/1+tan60°tan45°
✓3-1/1+✓3.1
✓3-1/✓3+1
Rationalizing
✓3-1.✓3-1/✓3+1.✓3-1
(✓3-1)^2/(✓3)^2-2
3+1-2✓3/3-1
4-2✓3/2
2(2-✓3)/2
2-✓3
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