Question

If :3sine +4 case and y=3cose - 4 sine then prove that x2 + y2 = 25.​

Answer 1

Step-by-step explanation:

Given :-

x= 3sine +4 cose and y=3cose - 4sine

To find:-

If x= 3sine +4 case and y=3cose - 4 sine then prove that x^2 + y^2 = 25.

Solution:-

Given that :

x= 3sine +4 cose

On squaring both sides

x^2 = (3sine +4 cose)^2

It is in the form of (a+b)^2

Where, a = 3 sine and b = 4 cose

We know that

(a+b)^2 =a^2+2ab+b^2

=>x^2 = (3sine)^2+2(3sine)(4cose)+(4cose)^2

x^2 = 9 sin^2 e +24 sine Cose +16 Cos^2 e----(1)

And

y=3cose - 4 sine

On squaring both sides then

y^2 = (3cose - 4 sine)^2

It is in the form of (a-b)^2

Where, a = 3 cose and b = 4 sine

We know that

(a-b)^2 =a^2-2ab+b^2

=>y^2 = (3cose)^2-2(3cose)(4sine)+(4sine)^2

y^2 = 9cos^2e -24sinecose +16sin^2e------(2)

On adding (1)&(2) then

x^2+y^2=

9 sin^2 e +24 sine Cose +16 Cos^2 e+9cos^2e -24sinecose +16sin^2e

x^2+y^2 = 9sin^2e+9cos^2e+16sin^2e+16cos^2e

x^2+y^2 = 9(sin^2e+cos^e)+16(sin^2e+cos^2e)

We know that

Sin^2 A + Cos^2 A = 1

=>x^2 +y^2 = 9(1)+16(1)

=>x^2 +y^2 = 9+16

x^2+y^2 = 25

Answer:-

If x= 3sine +4 case and y=3cose - 4 sine then prove that x^2 + y^2 = 25.

Used formulae:-

• (a+b)^2 =a^2+2ab+b^2
• (a-b)^2 =a^2-2ab+b^2
• Sin^2 A + Cos^2 A = 1