Question

find the value of 2 tan 45° + cos 60° - sin 30°​

Answer 1

$\LARGE\bold { \color{magenta}{ \underline{ \color{yellow}{\mathtt{Find:↓}}}}}$

$\large \bold \red{2 \: tan \: 45° + cos \: 60° - sin \: 30°}$

$\LARGE\bold { \color{magenta}{ \underline{ \color{yellow}{\mathtt{Solution:↓}}}}}$

We have to find, the value of:

$\large \bold {2 \: tan \: 45° + cos \: 60° - sin \: 30°= \: ?}$

$\bold{∴ 2 \:tan\:45 ° + cos\:60 ° - sin\:30°}$

$\bold{= 2(1) + \dfrac{1}{2} - \dfrac{1}{2} }$

Using the trigonometric identity:

${2\:tan\:45 ° = \bold{1}, \:cos\:60 ° = \dfrac{1}{2} \: \bold{and} \:sin\:30 ° = \dfrac{1}{2} }$

$\implies{2 + \dfrac{1}{2} - \dfrac{1}{2}}$

$\implies\Large\bold{\pink{\boxed{\displaystyle{2}}}}$

$∴ \bold{2 \:tan\:45 ° + cos \:60 ° - sin\:30 ° \implies\Large\bold{\orange{\boxed{\displaystyle{2}}}}}$

$\bold{Thus, \: the \: value \: of \: 2 \:tan\:45 ° + cos \:60 ° - sin\:30 °:}$

$\implies\Large\bold{\green{\boxed{\displaystyle{2}}}}$

⭐______________________⭐

Hopes it's helpful