Question

Find the value of : Root3tan 30+ root 2 sin 45 + 2/Root 3 sin 60 - 3cot 45

Answer 1

$\underline{\bf{TO \: FIND:-}}$

√3 tan30°+ √2 sin45° + 2/√3 sin60° - 3 cot 45°

$\\ \underline{\bf{SOLUTION :-}}$

= √3 tan 30° + √2 sin45° + 2/√3 sin 60° - 3 cot 45°

= √3 × 1/√3 + √2 × 1/√2 + 2/√3 × √3/2 - 3 × 1

= 1 + 1 + 1 - 3

= 0

Therefore, the value of the above equation is 0.

$\\ \underline{\bf{EXPLANATION:-}}$

• √3 tan 30° = √3 × 1/√3.... [∵tan30° = 1/√3]

• √2 sin45° = √2 × 1/√2.... [∵sin45° = 1/√2]

• 2/√3 sin 60° = 2/√3 × √3/2.... [∵sin60° = √3/2]

• 3 cot 45° = 3×1.... [∵cot45° = 1]

$\\ \underline{\bf{Extra \: information:- }}$

$\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ \: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1 \end{minipage}}$