Question

Find the value of tan 30 ×sin 60 +cos60

Answer 1

Dear Student,

Given question is about finding the total value of the given trigonometric identities.

So, apply the values of the following trivial identities for respective trigonometric functions that is,

$\bf{tan(30) =<strong> </strong>\dfrac{\sqrt{3}}{3}}$

$\bf{sin(60) = \dfrac{\sqrt{3}}{2}}$

$\bf{cos(60) = \dfrac{1}{2}}$

Apply the trivial identities of trigonometric functions into our original valued trigonometric identity equation that is;

$\bf{\dfrac{\sqrt{3}}{3} \times \dfrac{\sqrt{3}}{2} + \dfrac{1}{2}}$

$\bf{\dfrac{\sqrt{3} \times \sqrt{3}}{3 \times 2} + \dfrac{1}{2}}$

$\bf{\dfrac{3}{6} + \dfrac{1}{2}}$

$\bf{\dfrac{1}{2} + \dfrac{1}{2}}$

$\bf{\dfrac{1 + 1}{2}}$

$\bf{\dfrac{2}{2}}$

$\boxed{\bf{\underline{\therefore \quad tan(30) \times sin(60) + cos(60) = 1}}}$

Which is the required solution for this type of query.

Hope it helps you and clears your doubts for applying trivial identities to directly obtain the final value for  given trigonometric identity equation !!!!

Answer 2

tan30 X sin 60 + cos60

tan30= 1/$\sqrt{3}$

sin60= √3/2

cos60 = 1/2

1/√3 × √3/2 + 1/2

= 1/2 + 1/2

= 1