Question

cos45.cos15- sin45.sin15. evaluate this​

Answer 1

Since,

cos(A+B)=cosA.cosB - sinA.sinB

so, cos45.cos15- sin45.sin15=cos(45+15)=cos60=1/2=0.50

Answer 2

Answer:

cos45.cos15- sin45.sin15 $=\frac{1}{2}$.

Step-by-step explanation:

Trigonometry formulas are sets of different formulas involving trigonometric identities, used to solve problems based on the sides and angles of a right-angled triangle. These trigonometry formulas include trigonometric functions like sine, cosine, tangent, cosecant, secant, cotangent for given angles.

The sum and difference identities include the trigonometry formulas of sin(x + y), cos(x - y), cot(x + y), etc.

sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

tan(x + y) = (tan x + tan y)/(1 - tan x • tan y)

sin(x – y) = sin(x)cos(y) - cos(x)sin(y)

cos(x – y) = cos(x)cos(y) + sin(x)sin(y)

tan(x − y) = (tan x - tan y)/(1 + tan x • tan y)

Given: cos45.cos15- sin45.sin15.

Find:  Evaluate the trigonometry equation.

$cos45.cos15- sin45.sin15$

Use formula cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

therefore

$cos45.cos15- sin45.sin15\\=cos(45+15)\\=cos60\\=\frac{1}{2}$

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