IDNLearn.com offers a seamless experience for finding and sharing knowledge. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.
Sagot :
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 value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.