Question

Find the exact value of the expression by using appropriate identities. Do not use a calculator. $\frac{tan 77 + tan 43}{1 - tan 77.tan 43}$

Answer 1

Answer:

$-\sqrt{3}$

Step-by-step explanation:

From Trigonometric Identity

$Tan (A+B)=\frac{tan A + tan B}{I-tan A\cdot tan B}$

Therefore comparing $\frac{tan 77 + tan 43}{I-tan 77\cdot tan 43}$ with the above:

A=77, B=43

$\frac{tan 77 + tan 43}{I-tan 77\cdot tan 43}=Tan (77+43)$

                  =Tan 120

Tan is Negative in the Second Quadrant

Tan 120 =$-\sqrt{3}$

Answer 2

Answer:

Step-by-step explanation:

Remember from Trig. identity:

Tan(a + b) = (tan a + tan b)/1 - tana × tan b

From the above,

(tan 77 + tan 43)/1 - tan 77 × tan 43

Comparing Both equations on the LHS,

a = 77

b = 43

Therefore, on the right hand side;

Tan (a + b) = tan (77 + 43)

= tan 120

Tan θ = sin θ/cos θ

Sin 120 = (root3)/2

Cos 120 = -1/2

Therefore, tan 120 = (root3)/2 × -2/1

= -(root3)