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Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?
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Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?
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Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?
Solution:
Step 1: Rewrite the given trigonometric expressions in terms of basic trigonometric functions.
sin^2 30 = (sin 30)^2 = (1/2)^2 = 1/4
cos^2 45 = (cos 45)^2 = (1/√2)^2 = 1/2
tan^2 30 = (sin 30/cos 30)^2 = (1/√3)^2 = 1/3
sin^2 90 = (sin 90)^2 = 1
cos^2 90 = (cos 90)^2 = 0
Step 2: Substitute the values obtained in step 1 into the given expression.
sin^2 30 cos^2 45 + 4tan^2 30 + 1/2 sin^2 90 - 2cos^2 90
= (1/4) x (1/2) + 4 x (1/3) + 1/2 - 2(0)
= 1/8 + 4/3 + 1/2
= (3/24) + (32/24) + (12/24)
= 47/24
= 1 23/24
Therefore, the value of the given expression is 1 23/24.
Explanation:
The given expression involves trigonometric functions of angles 30, 45 and 90 degrees. We use the basic trigonometric identities to rewrite the expressions in terms of basic trigonometric functions. Then, we substitute the values obtained in the given expression and simplify it to obtain the final result.
Step 1: Rewrite the given trigonometric expressions in terms of basic trigonometric functions.
sin^2 30 = (sin 30)^2 = (1/2)^2 = 1/4
cos^2 45 = (cos 45)^2 = (1/√2)^2 = 1/2
tan^2 30 = (sin 30/cos 30)^2 = (1/√3)^2 = 1/3
sin^2 90 = (sin 90)^2 = 1
cos^2 90 = (cos 90)^2 = 0
Step 2: Substitute the values obtained in step 1 into the given expression.
sin^2 30 cos^2 45 + 4tan^2 30 + 1/2 sin^2 90 - 2cos^2 90
= (1/4) x (1/2) + 4 x (1/3) + 1/2 - 2(0)
= 1/8 + 4/3 + 1/2
= (3/24) + (32/24) + (12/24)
= 47/24
= 1 23/24
Therefore, the value of the given expression is 1 23/24.
Explanation:
The given expression involves trigonometric functions of angles 30, 45 and 90 degrees. We use the basic trigonometric identities to rewrite the expressions in terms of basic trigonometric functions. Then, we substitute the values obtained in the given expression and simplify it to obtain the final result.
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Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?.
Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?.
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