4 years ago

Prove the identity I NEED TO KNOW FAST AS POSSIBLE

Mathematics

1 answer:

antoniya [11.8K]4 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sin²Θ = 1 - cos²Θ , cos²Θ = 1 - sin²Θ

Consider the left side

(sinΘ + cosΘ)(1 - sinΘcosΘ) ← distribute

= sinΘ(1 - sinΘcosΘ) + cosΘ(1 - sinΘcosΘ)

= sinΘ - sin²ΘcosΘ + cosΘ - sinΘcos²Θ

= sinΘ - (1 - cos²Θ)cosΘ + cosΘ - sinΘ(1 - sin²Θ)

= sinΘ - cosΘ + cos³Θ + cosΘ - sinΘ + sin³Θ ← collect like terms

= sin³Θ + cos³Θ

= right side ⇒ proven

You might be interested in

What is the y-value when x equals 25? y= 650 - 15(x)

yarga [219]

Answer:

y= 275 when x is 25

5 0

3 years ago

There are 82 trees at a park. Half of the trees are pecan trees and the

Marrrta [24]

Answer:

41 oak tree

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

GEOMETRY// Area? Also please provide an explanation(:

Zina [86]

Answer:

A = 80

Step-by-step explanation:

B = 8

H = 10

Area of a Parallelogram = B x H = 8 x 10 = 80

8 0

3 years ago

Which expressions are equivalent to (2^2-9) (x + 3)?

mestny [16]

Answer:

$(x^2-3^2)(x+3)$

$(x-3)(x+3)(x+3)$

$(x-3)(x+3)^2$

Step-by-step explanation:

Given

$(x^2-9)(x+3)$

Required

Select 3 equivalent expressions

$(x^2-9)(x+3)$

Express 9 as 3^2

$(x^2-3^2)(x+3)$ --- This is one equivalent expression

Take $x^2 - 3^2$ as difference of two squares

$(x-3)(x+3)(x+3)$ -- This is another equivalent expression:

Solving further:

$(x-3)(x+3)(x+3)$ becomes

$(x-3)(x+3)^2$ -- This is another equivalent expression:

Hence, the equivalent expressions are:

$(x^2-3^2)(x+3)$

$(x-3)(x+3)(x+3)$

$(x-3)(x+3)^2$

7 0

3 years ago

John has 15 t shirts. 6 black, 3 red, 2 purple, 2 dark blue, 1 light blue, 1 purple

Troyanec [42]

Answer:

ok.... what is the question here....?? ;-;

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers