Question

What is the value of tan 45º + sin 60°- cos 30° as per Trigonometrical ratio?
b) 2
d) v​

Answer 1

See the attachment

Hope this helped you

Answer 2

Answer:

The value of tan45° + sin60° - cos30° = 1

Step-by-step explanation:

$\Diamond$ Trigonometric ratios are ratios of sides of a right-angled triangle

$\Diamond$ There are 6 trigonometric ratios namely :

1. sine $\implies$ sin
2. cosine $\implies$ cos
3. tangent $\implies$ tan
4. cosecant $\implies$ cosec
5. secant $\implies$ sec
6. cotangent $\implies$ cot

$\Diamond$ sin, cos, tan, cosec, sec and cot are the abbreviations of the trigonometric ratios

$\Diamond$ The table given below shows the various values of the trigonometric ratios

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 65^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty   \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{\sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}} [tex]</p><p></p><p>[tex]\Diamond$ Hence

tan45° = 1

sin60° = $\dfrac{\sqrt{3}}{2}$

cos30° = $\dfrac{\sqrt{3}}{2}$

Substituting these values we get,

tan45° + sin60 - cos30

= 1 + $\dfrac{\sqrt{3}}{2}$ - $\dfrac{\sqrt{3}}{2}$

= 1 + 0

= 1