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(ii) sin^2 (2 deg) + sin^2 (3 deg) + sin^2 (88 deg) + sin^2 (87 deg) = 2

2 Answers

2 votes
0.0099 is the answer hopefully that helps.
User Vitorrio Brooks
by
9.4k points
5 votes

Answer: bellow .

Explanation:

To find the value of sin^2(2 deg) + sin^2(3 deg) + sin^2(88 deg) + sin^2(87 deg), we can use the trigonometric identity:

sin^2(x) + cos^2(x) = 1

Since the question is asking for the sum of four terms, we can use this identity to simplify the expression:

sin^2(2 deg) + sin^2(3 deg) + sin^2(88 deg) + sin^2(87 deg) = 1 - cos^2(2 deg) + 1 - cos^2(3 deg) + 1 - cos^2(88 deg) + 1 - cos^2(87 deg)

Next, let's use the fact that cos(x) = sin(90 deg - x):

= 1 - cos^2(2 deg) + 1 - cos^2(3 deg) + 1 - cos^2(2 deg) + 1 - cos^2(3 deg)

Now, we can use the identity sin^2(x) = 1 - cos^2(x):

= 1 - cos^2(2 deg) + 1 - cos^2(3 deg) + 1 - cos^2(2 deg) + 1 - cos^2(3 deg)

= 4 - (cos^2(2 deg) + cos^2(3 deg) + cos^2(2 deg) + cos^2(3 deg))

= 4 - 2(cos^2(2 deg) + cos^2(3 deg))

Now, we can substitute the values of cos(2 deg) and cos(3 deg) using a calculator or trigonometric tables. After calculating the values, we can plug them back into the expression:

= 4 - 2(0.99939^2 + 0.99863^2)

= 4 - 2(0.99878 + 0.99727)

= 4 - 2(1.99505)

= 4 - 3.9901

= 0.0099

Therefore, sin^2(2 deg) + sin^2(3 deg) + sin^2(88 deg) + sin^2(87 deg) is approximately equal to 0.0099.

User Fernando Montoya
by
8.6k points

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