Question

If sin A+ cos A= 1, then the value of 3 sin A cos A is:​

Answer 1

$\large\underline{\sf{Solution-}}$

Given Trigonometric equation is

$\rm :\longmapsto\:sinA + cosA = 1$

On squaring both sides, we get

$\rm :\longmapsto\: {(sinA + cosA)}^{2} = {1}^{2}$

$\rm :\longmapsto\: {(sinA)}^{2} + {(cosA)}^{2} + 2sinA \: cosA \: = \: 1$

$\rm :\longmapsto\: {sin}^{2}A + {cos}^{2}A + 2sinA \: cosA \: = \: 1$

$\rm :\longmapsto\: 1 + 2sinA \: cosA \: = \: 1$

$\rm :\longmapsto \: 2sinA \: cosA \: = \: 1 - 1$

$\rm :\longmapsto \: 2sinA \: cosA \: = \: 0$

$\bf\implies \:sinA \: cosA \: = \: 0$

Hence,

$\bf\implies \:3 \: sinA \: cosA \: = \: 0$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

FORMULA USED

$\purple{\rm :\longmapsto\:\boxed{\tt{ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}}$

$\purple{\rm :\longmapsto\:\boxed{\tt{ {sin}^{2}x + {cos}^{2}x = 1}}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Additional Information:-

Relationship between sides and T ratios

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

Co-function Identities

sin (90°−x) = cos x

cos (90°−x) = sin x

tan (90°−x) = cot x

cot (90°−x) = tan x

sec (90°−x) = cosec x

cosec (90°−x) = sec x

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1

Answer 2

Question:-

If sinA + cosA = 1, then the value of 3sinA cosA is:

Given:-

Trigonometric Equation:

⇒ sinA + cosA = 1.

To Find:-

• The value of 3sinA cosA.

Solution:-

sinA + cosA = 1

Squaring on Both sides:

(sinA + cosA)² = (1)²

sin²A + cos²A + 2sinA cosA = 1

1 + 2sinA cosA = 1

2sinA cosA = 1 – 1

2sinA cosA = 0

$\sf \large sinA \: cos A = \frac{0}{2} = 0 \: \: \: \: - - > (1)$

We have to Find 3sinA cosA:

= 3 × 0 (∵ From Equation 1 )

= 0.

Answer:-

$\sf \large { \boxed{ \purple{ \sf3sinA \: cos A = 0.}}}$

Hope you have satisfied. ⚘