Question

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Answer 1

Required Answer:-

Given to evaluate:

• $\rm \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \sin(59 \degree) \sec(31 \degree)$

Solution:

This question can be solved by using complementary angle formula.

Let's know them.

$\rm \star \sin(90 \degree - \alpha )= \cos( \alpha )$

$\rm \star \cos(90 \degree - \alpha )= \sin( \alpha )$

Using this formula, we will solve the problem.

Here comes the solution.

$\rm \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \sin(59 \degree) \sec(31 \degree)$

$\rm = \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \dfrac{ \sin(59 \degree) }{ \cos(31 \degree) }$

Now, apply the formula here,

$\rm = \dfrac{ \sin(80 \degree) }{ \cos(90 \degree - 80 \degree) } + \dfrac{ \sin(90\degree - 31 \degree) }{ \cos(31 \degree) }$

Evaluate,

$\rm = \dfrac{ \sin(80 \degree) }{ \sin( 80 \degree) } + \dfrac{ \cos(31 \degree) }{ \cos(31 \degree) }$

Cancel out,...

$\rm = 1 + 1$

$\rm = 2$

Hence,

$\rm \star \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \sin(59 \degree) \sec(31 \degree) = 2$

Answer:

• $\rm \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \sin(59 \degree) \sec(31 \degree) = 2$

Answer 2

Required Answer:-

Given to evaluate:

$\rm \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \sin(59 \degree) \sec(31 \degree)$

Solution:

This question can be solved by using complementary angle formula.

Let's know them.

$\rm \star \sin(90 \degree - \alpha )= \cos( \alpha )⋆sin(90°−α)=cos(α)$

$\rm \star \cos(90 \degree - \alpha )= \sin( \alpha )⋆cos(90°−α)=sin(α)</p><p>$

Using this formula, we will solve the problem.

Here comes the solution.

$\rm \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \sin(59 \degree) \sec(31 \degree) </p><p>cos(10°)</p><p>sin(80°)</p><p>$

$\rm = \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \dfrac{ \sin(59 \degree) }{ \cos(31 \degree) } </p><p>$

Now, apply the formula here,

$\rm = \dfrac{ \sin(80 \degree) }{ \cos(90 \degree - 80 \degree) } + \dfrac{ \sin(90\degree - 31 \degree) }{ \cos(31 \degree) }$

Evaluate,

$\rm = \dfrac{ \sin(80 \degree) }{ \sin( 80 \degree) } + \dfrac{ \cos(31 \degree) }{ \cos(31 \degree) }$

Cancel out,...

$\rm = 1 + 1=1+1$

$\rm = 2=2$

Hence,

$\rm \star \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \sin(59 \degree) \sec(31 \degree)$

Answer:

$\rm \dfrac{ \sin(80 \degree) }{ \cos(10 \degree) } + \sin(59 \degree) \sec(31 \degree)$