Question

if tan a=√3 and tan b=1/√3 0 less than a, b less than 90 find the value of cot (a+b)
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Answer 1

★${\underline{\underline{\bold{Given:-}}}}$

• $\sf{tan\:a=\sqrt{3}}$
• $\sf{tan\:b=\dfrac{1}{\sqrt{3}}}$
• 0 < a,b < 90

★${\underline{\underline{\bold{To\: find:-}}}}$

• Value of cot (a+b).

★${\underline{\underline{\bold{Solution:-}}}}$

✞${\sf{\purple{tan\:a=\sqrt{3}}}}$

$\to\sf{tan\:a=tan\:60\degree}$

$\to\sf{a=60\degree}$

✞${\sf{\purple{tan\:b=\dfrac{1}{\sqrt{3}}}}}$

$\to\sf{tan\:b=tan\:30\degree}$

$\to\sf{b=30\degree}$

Now, find the value of cot(a+b) :-

$\to\sf{cot(a+b)}$

• Put a = 60° and b = 30°

$\to\sf{cot(60+30)}$

$\to\sf{cot\:90\degree}$

$\to\sf{0\:[Answer]}$

________________

More information :-

★ Some trigonometric values :-

• sin30° = 1/2
• sin45° = 1/√2
• sin60° = √3/2
• cos30° = √3/2
• cos45° = 1/√2
• cos60° = 1/2
• tan30° = 1/√3
• tan45° = 1
• tan60° = √3

★Some trigonometric identities :-

• sin²A + cos²A = 1

• 1 + tan²A = sec²A

• 1 + cot²A = cosec²A

• cos²A - sin²A = cos2A

Answer 2

${\red{\underline{\boxed{\sf{QUESTION :}}}}}$

if tan A=√3 and tan B=1/√3 0 less than A, B less than 90°, find the value of cot (a+b) .

${\blue{\underline{\boxed{\sf{SOLUTION :}}}}}$

$\longrightarrow$Tan A = √3 = Tan 60°

$\longrightarrow$ ${\boxed{\blue{\sf{ A = 60°}}}}$

$\longrightarrow$Tan B = 1/√3 = Tan 30°

$\longrightarrow$ ${\boxed{\purple{\sf{B = 30°}}}}$

$\longrightarrow$Cot(A+B) = Cot(60+30)°

$\longrightarrow$ ${\red{\boxed{\underline{\sf{Cot90° = 0 .}}}}}$

Hence, the value of cot(A+B) is 0 .

${\green{\underline{\boxed{\sf{Some \: Trigonometry \: Identities :}}}}}$

• Sin²θ + Cos²θ = 1

• 1 + Tan²θ = Sec²θ

• 1 + Cot²θ = Cosec²θ .