tara36203
Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

cos 15 - sin 15 = 1/2


prove that :​

Sagot :

spectrojamz

Answer:

Cos(15) = Cos(45-30)

Sin(15) = Sin(45-30)

Cos(45-30) - Sin(45-30)

Simplifying both brackets

Recall

Cos(A+B) = CosACosB - SinASinB (For cosine... The sign is always the opposite during expansion. If you look... Cos(A+B) became negative during its expansion;So if It was Cos(A–B)... Its expansion is CosACosB + SinASinB)]

Sin(A+B) = SinACosB + CosASinB

Now let's go!

Cos(45-30) = Cos45Cos30 + Sin45Sin30

From Trig

Cos45 = 1/√2

Cos30 = √3/2

Sin45 = 1/√2

Sin30 = 1/2

Substituting

Cos(45-30) = (1/√2).(√3/2) + (1/√2).(1/2)

= √3/(2√2) + 1/(2√2)

= 1 + √3/(2√2).

For

Sin(45 - 30)

= Sin45cos30 – Cos45Sin30

= (1/√2).(√3/2) – (1/√2).(1/2)

= √3/(2√2) – 1/2√2

= √3 – 1/(2√2)

So the question was

Cos15 - Sin15

Substituting...

1 + √3 / 2√2 – (√3 - 1)/ 2√2

When the Minus interacts with the parenthesis

We have

1 + √3 - √3 + 1 / (2√2)

= 2/2√2

= 1/√2.

THE ANSWER IS 1/√2 AND NOT 1/2.

YOU CAN VERIFY THIS WITH YOUR CALCULATOR ALSO.

YOU'LL HAVE 0.7071 WHICH IS SAME AS 1/√2.

HAVE A GREAT DAY!

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.