Question

if cos a = 2/5 find 2cosa sina​

Answer 1

• 2 cos A sin A = 4√21/5.

Step-by-step explanation:

To find:-

• Vale of 2 cos A sin A .

Solution:-

Given that,

cos A = 2/5

◆ cos θ = Base/Hypotenuse

Base = 2

Hypotenuse = 5

◆ sin θ = Perpendicular/Hypotenuse

• We do not have Perpendicular.

According to Pythagoras theorem

Perpendicular² = Hypotenuse² - Base²

➝ Perpendicular² = (5)² - (2)²

➝ Perpendicular² = 25 - 4

➝ Perpendicular² = 21

➝ Perpendicular = √21

Sin A = Perpendicular/Hypotenuse

Sin A = √21/5

We want ,

➝ 2 cos A sin A

➝ 2 × 2/5 × √21/5

➝ 4√21/5

Therefore,

2 cos A sin A = 4√21/5.

___________________

More ratio's:-

• tan θ = Perpendicular/Base.
• cot θ = Base/Perpendicular.
• Sec θ = Hypotenuse/Base.
• Cosec θ = Hypotenuse/Perpendicular.

Answer 2

$\large{ \sf \underline{ \blue{ ╬ \: Question\: ╬}}} </h2><h2>$

if cos a = 2/5 find 2cosa sina.

$\large{ \sf \underline{ \blue{ ╬ \: find \: ╬}}}$

2cosa.sina=?

$\large{ \sf \underline{ \blue{ ╬ \: given \: that \: ╬}}}$

Cos a = 2/5

$\large{ \sf \underline{ \blue{ ╬ \: solution \: ╬}}}$

We know that cos = b/h

so here

hypotenuse (h) =5

base (b) =2

perpendicular (p) = ?

__________________

Now by using Pythagoras theorem .

$\bf H^2 =B^2+P^2 \\ </h3><h3> \bf \ P^2= (5)^2-(2)^2 \\ </h3><h3> \bf P^2 = 25 -4 \\ </h3><h3> \bf P^2 = 21 \\ </h3><h3> \bf P =√21$

After that

We know that

• sin a = p/h

so sin a = √21/5

$\large{ \sf \underline{ \pink{ ╬ \: putting \: the \: value \: of \: cos \: a \: \: and\: \: sin \: a ╬ \: \: }}} </p><p>$

☞ 2 x 2/5 × √21/5

☞= 4√21/25