tara36203
Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A 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!

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.