Find the value of this expression: sin 45 sin 15 . the second step = a. 1 sin 60 – sin 30 2 b. 1 cos 60 cos 30 2 c. 1 sin 60 sin 30 2 d. 1 cos 60 cos 30 find the value of this expression: cos 75 – cos 15 . the second step = a. –2 cos 45 cos 30 b. –2 sin 45 sin 30 c. 2 sin 45 cos 30 d. 2 cos 45 sin 30

Given expression is sin(45)sin(15)

this expression best matches with left side of the formula:

2 sin(A) sin(B)= cos(A-B) - cos(A+B)

so we can plug given angles 45 and 15 there

2 sin(45) sin(15)= cos(45-15) - cos(45+15)

2 sin(45) sin(15)= cos(30) - cos(60)

sin(45) sin(15)= [cos(30) - cos(60)]/2

We are getting negative sign and cos in the solution while none of the given choices have same situation so answer will be none of them.

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For cos(75)-cos(15), we will use formula:

Now plug the given angles

Hence choice B is correct.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

you should at least use a calculater

step-by-step explanation: