if tan A=1 and Tan B=root 3 then find the value of CosA*cosB-sinA*SinB
Answers & Comments
dhruvsh
Tan a = 1 Tan A = tan 45 A = 45. Now, Tan b = root 3 Tan b = tan 60. B = 60.
Now , Cos a * cos b - sin A * sin B = cos 45 * cos 60 - sin 45 * sin 60 = 1/root 2 * 1/2 - 1/root 2 * root 3 /2 = 1 /root 2 ( 1/2 - root 3 /2) = 1/root 2 * 1 - root 3 /2 = 1 - root 3 / 2 root 2.
Answers & Comments
Tan A = tan 45
A = 45.
Now,
Tan b = root 3
Tan b = tan 60.
B = 60.
Now ,
Cos a * cos b - sin A * sin B
= cos 45 * cos 60 - sin 45 * sin 60
= 1/root 2 * 1/2 - 1/root 2 * root 3 /2
= 1 /root 2 ( 1/2 - root 3 /2)
= 1/root 2 * 1 - root 3 /2
= 1 - root 3 / 2 root 2.
Tan A = 1 = p/b
p= 1 , b= 1 , h=?
we know that,
h²= p²+b²= (1)²+ (1)²=2
h= ✓2
Tan B = ✓3 = p/b
p= ✓3, b= 1 , h= ?
h² = (p)² + (b)² = (✓3)² + (1)² = 3 + 1 = 4
h= ✓4 = 2
Therefore,
Sin A = P/h = 1 /✓2
Cos A = b/h = 1/✓2
CosB = b/h = 1/2
SinB = p/h = ✓3/2
Therefore,
CosA × Cos B - SinA × CosB= 1/✓2× 1/2 - 1/✓2 × ✓3/2.
=1-✓3/2✓2
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