Question

If 'a' is a real constant and A, B, C are variable anglesand

tan A + a tan B + $\sqrt { \mathrm { a } ^ { 2 } + 4 }$ tan C = 6a then the least

value of tan² A + tan² B + tan²C is –

• A. 6
• B. 10
• C. 12
• D. 3

Answer 1

Answer: (C)

12

Answer 2

Given relation can be written as the vector expression

$\left( \sqrt { a ^ { 2 } - 4 } \hat { i } + a \hat { j } + \sqrt { a ^ { 2 } + 4 } \hat { k } \right)$. $( \tan \mathrm { A } \hat { \mathrm { i } } + \tan \mathrm { B } \hat { \mathrm { j } } + \tan \mathrm { C } \hat { \mathrm { k } } )$

$\sqrt { a ^ { 2 } - 4 + a ^ { 2 } + a ^ { 2 } + 4 }$ $\sqrt { \tan ^ { 2 } \mathrm {~A} + \tan ^ { 2 } \mathrm {~B} + \tan ^ { 2 } \mathrm { C } }$

(cos q) = 6a

tan² A + tan² B + tan² C = 12 sec² q ³ 12

least value of tan² A + tan² B + tan² C is 12.