Question

Chapter
1 Find the values of:
(1) sina 60° - cos2 45° + 3 tan2 30°​

Answer 1

TO FIND :–

• The value of sin(60°) - cos²(45°) + 3 tan²(30°) = ?

SOLUTION :–

• We know that –

▪︎ sin(60°) = √3/2

▪︎ cos(45°) = 1/√2

▪︎ tan(30°) = 1/√3

• Let –

⇒ P = sin(60°) - cos²(45°) + 3 tan²(30°)

• Now put the values –

⇒ P = √3/2 - (1/√2)² + 3 (1/√3)²

⇒ P = √3/2 - ½ + 3(⅓)

⇒ P = √3/2 - ½ +1

⇒ P = √3/2 + ½

⇒ P = (√3 + 1)/2

• Hence –

⇒ sin(60°) - cos²(45°) + 3 tan²(30°) = (√3 + 1)/2

More Information :–

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

Answer 2

Answer:

$\rm\dfrac{5}{4}$

Step-by-step explanation:

Question:

Find the value of: $\bf{sin^260° - cos^245° + 3tan^2 30°}$

We know that,

• sin60°=$\rm\dfrac{√3}{2}$

• cos45° = $\rm\dfrac{1}{√2}$

• tan30° = $\rm\dfrac{1}{√3}$

So, apply the values:

$\rm\dfrac{(√3)^2}{2^2}$- $\rm\dfrac{1}{(√2)^2}$+3 $\times$ $\rm\dfrac{1}{(√3)^2}$

$\rm\dfrac{3}{4}$-$\rm\dfrac{1}{2}$+3$\times$ $\rm\dfrac{1}{3}$

$\rm\dfrac{3}{4}$-$\rm\dfrac{1}{2}$ +1

$\rm\dfrac{3}{4}$+$\rm\dfrac{1}{2}$

$\implies$ $\rm\dfrac{5}{4}$

Final answer:

$\rm\dfrac{5}{4}$

Know more:

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$