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Prove that 1/cosec theta -cot theta -1/sin theta=1/sin theta -1/cosec theta cot theta?
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Prove that 1/cosec theta -cot theta -1/sin theta=1/sin theta -1/cosec ...
Proof: 1/cosec theta - cot theta - 1/sin theta = 1/sin theta - 1/cosec theta cot theta
Step 1: Rewrite all trigonometric functions in terms of sin and cos
We know that:
- cosec(theta) = 1/sin(theta)
- cot(theta) = cos(theta)/sin(theta)
Substituting these values, we get:
- 1/cosec(theta) - cot(theta) - 1/sin(theta) = 1/sin(theta) - 1/cosec(theta) * cot(theta)
Step 2: Simplify the left-hand side of the equation
- 1/cosec(theta) - cot(theta) - 1/sin(theta) = 1/sin(theta) - cos(theta)/sin(theta) - 1/sin(theta)
- 1/cosec(theta) - cot(theta) - 1/sin(theta) = -cos(theta)/sin(theta)
- 1/cosec(theta) - cot(theta) - 1/sin(theta) = -1/sin(theta) * cos(theta)
Step 3: Simplify the right-hand side of the equation
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = 1/sin(theta) - 1/(1/sin(theta)) * (cos(theta)/sin(theta))
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = 1/sin(theta) - sin(theta)/cos(theta)
Step 4: Combine like terms on the right-hand side
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = (cos(theta)/cos(theta)*sin(theta)) - (sin(theta)/cos(theta)*sin(theta))
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = (cos(theta)*sin(theta) - sin(theta))/sin(theta)*cos(theta)
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = sin(theta)*(cos(theta)-1)/sin(theta)*cos(theta)
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = (cos(theta)-1)/cos(theta)
Step 5: Simplify the right-hand side further
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = cos(theta)/cos(theta) - 1/cos(theta)
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = 1/cos(theta) - 1/cosec(theta)
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = 1/cosec(theta) * sin(theta) - 1/cosec(theta)
- 1/sin(theta) - 1/cosec(theta) * cot(theta) = 1/cosec(theta) * (sin(theta) - cot(theta)))
Step 6: Substitute the left-hand side of the equation with the right-hand side
- -cos(theta)/sin(theta
Community Answer
Prove that 1/cosec theta -cot theta -1/sin theta=1/sin theta -1/cosec ...
Can you plz upload a pic of this queation.
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Prove that 1/cosec theta -cot theta -1/sin theta=1/sin theta -1/cosec theta cot theta?
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Prove that 1/cosec theta -cot theta -1/sin theta=1/sin theta -1/cosec theta cot theta? 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 Prove that 1/cosec theta -cot theta -1/sin theta=1/sin theta -1/cosec theta cot theta? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that 1/cosec theta -cot theta -1/sin theta=1/sin theta -1/cosec theta cot theta?.
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