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If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos theta=3?
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If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos thet...
Verification of the Trigonometric Expression:
To show that 2sin theta - 3cos theta / 4sin theta - 9cos theta equals 3 when sec theta = 13/5, we will follow the steps below:
Step 1: Finding sin theta and cos theta
Given that sec theta = 13/5, we know that sec theta = 1/cos theta. Therefore, cos theta = 5/13.
Using the Pythagorean identity sin^2 theta + cos^2 theta = 1, we can find sin theta:
sin^2 theta + (5/13)^2 = 1
sin^2 theta = 1 - 25/169
sin theta = sqrt(144/169) = 12/13
Step 2: Substituting sin theta and cos theta into the expression
Now, substitute sin theta = 12/13 and cos theta = 5/13 into the expression:
(2(12/13) - 3(5/13)) / (4(12/13) - 9(5/13))
= (24/13 - 15/13) / (48/13 - 45/13)
= 9/13 / 3/13
= 3
Therefore, the expression 2sin theta - 3cos theta / 4sin theta - 9cos theta equals 3 when sec theta = 13/5.
To show that 2sin theta - 3cos theta / 4sin theta - 9cos theta equals 3 when sec theta = 13/5, we will follow the steps below:
Step 1: Finding sin theta and cos theta
Given that sec theta = 13/5, we know that sec theta = 1/cos theta. Therefore, cos theta = 5/13.
Using the Pythagorean identity sin^2 theta + cos^2 theta = 1, we can find sin theta:
sin^2 theta + (5/13)^2 = 1
sin^2 theta = 1 - 25/169
sin theta = sqrt(144/169) = 12/13
Step 2: Substituting sin theta and cos theta into the expression
Now, substitute sin theta = 12/13 and cos theta = 5/13 into the expression:
(2(12/13) - 3(5/13)) / (4(12/13) - 9(5/13))
= (24/13 - 15/13) / (48/13 - 45/13)
= 9/13 / 3/13
= 3
Therefore, the expression 2sin theta - 3cos theta / 4sin theta - 9cos theta equals 3 when sec theta = 13/5.
Community Answer
If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos thet...
Hey can I pls CHK the question I think there is something wrng
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If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos theta=3?
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If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos theta=3? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos theta=3? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos theta=3?.
If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos theta=3? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos theta=3? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sec theta=13/5 show that 2sin theta-3cos theta/4sin theta-9cos theta=3?.
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