Question

If tan (a-b) is root 3 and sina is 1 find a and b

Answer 1

Answer:-

Given:

tan (a - b) = √3

We know that,

tan 60 = √3

Hence,

tan (a - b) = tan 60°

On Comparing both sides,

→ a - b = 60° -- equation (1)

And also given that,

Sin a = 1

1 in terms of sin is sin 90°.

→ Sin a = Sin 90°

→ a = 90°

Putting the value of a in equation (1) we get,

→ 90° - b = 60°

→ 90° - 60° = b

→ b = 30°

Hence, the measurements of a and b are 90° , 30°.

Answer 2

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{ANSWER}}}}⋆$

• The measurement of a = 90°.
• The measurement of b = 30°.

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{EXPLANATION}}}}⋆$

$\blue{\bold{\underline{\underline{Given}}}}</p><p>$

• tan (a - b) = √3
• sin a = 1

We know that,

• tan 60 = √3

Hence,

• tan (a - b) = tan 60°

$\blue{\bold{\underline{\underline{On \: comparing \: both \: sides}}}}$

• a - b = 60° ------------ equation (i)

$\blue{\bold{\underline{\underline{Also \: given}}}}$

• Sin a = 1

=> a = Sin 90°/Sin

=> a = 90°

$\blue{\bold{\underline{\underline{Putting \: the \: value \: of \: a \: in \: equation \: (i)}}}}$

90° - b = 60°

=> 90° - 60° = b

=> b = 30°

$\blue{\bold{\underline{\underline{Answer}}}}$

• The measurement of a = 90°
• The measurement of b = 30°