Question

If x=2sinƟ and y=2cosƟ, and sinƟcosƟ=2 then find (x+y)
²​

Answer 1

Question :

If $\sf{x = 2sin\:\theta}$, $\sf{y = 2cos\:\theta}$ and $\sf{sin\:\theta cos\:\theta = 2}$ then find the value of $\sf{(x + y)^{2}}$

Answer :

• The value of the equation $\sf{(x + y)^{2}}$ is 20.

Explanation :

Given :

• The value of $\sf{x = 2sin\:\theta}$.
• The value of $\sf{y = 2cos\:\theta}$.
• The value of $\sf{(x + y)^{2}}$.

To find :

• The value of the equation $\sf{(x + y)^{2}}$ = ?

Knowledge required :

• $\sf{sin^{2}\theta + cos^{2}\theta = 1}$
• $\sf{(a + a)^{2}) = a^{2} + b^{2} + 2ab}$

Solution :

By substituting the values of x and y in the given equation, we get :

$:\implies \sf{(x + y)^{2}} \\ \\ :\implies \sf{(x + y)^{2} = (2sin\:\theta + 2cos\:\theta)^{2}} \\ \\ :\implies \sf{(x + y)^{2} = 4sin^{2}\theta + 4cos^{2}\theta + 2 \times 2sin\:\theta \times 2cos\:\theta} \\ \\ :\implies \sf{(x + y)^{2} = 4(sin^{2}\theta + cos^{2}\theta) + 2 \times 2sin\:\theta \times 2cos\:\theta} \\ \\ :\implies \sf{(x + y)^{2} = 4(1) + 8sin\:\theta cos\:\theta} \\ \\ :\implies \sf{(x + y)^{2} = 4(1) + 8(2)} \\ \\ :\implies \sf{(x + y)^{2} = 4 + 16} \\ \\ :\implies \sf{(x + y)^{2} = 20} \\ \\ \underline{\underline{\therefore \sf{(x + y)^{2} = 20}}}$

Therefore,

• The value of the equation $\sf{(x + y)^{2}}$ = 20

Answer 2

$\huge{\boxed{\bold{Question}}}$

If x=2sinƟ and y=2cosƟ, and sinƟcosƟ=2 then find (x+y)²

$\boxed { \bold{ \tt \: solution}} \\ \\ \rm \longmapsto \: (x + y) ^{2} \\ \\ \\ \longmapsto \rm \: (x + y) ^{2} = (2sin \theta + 2cos \theta) ^{2} \\ \\ \\ \longmapsto \rm(x + y) ^{2} = 4sin ^{2} \theta \: + 4cos ^{2} \theta + 2 \times 2sin \theta \times 2cos \\ \\ \\ \longmapsto \rm \: (x + y) ^{2} = 4sin ^{2} \theta \: + cos ^{2} \theta) + 2 \times 2sin \theta \times 2cos \theta \\ \\ \\ \longmapsto \rm \: (x + y) ^{2} = 4(1) + 8sin \theta \: cos \theta \\ \\ \\ \longmapsto \rm \: (x + y) ^{2} = 4(1) + 8(2) \\ \\ \\ \longmapsto \rm \: (x + y) ^{2} = 4 + 16 \\ \\ \\ \longmapsto \rm(x + y) ^{2} = 20 \\ \\ \\ \longmapsto \rm(x + y) ^{2} = 20 \boxed { \bold{ \sf answer}}$