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1 cosecA-cotA/1 cosecA cotA?
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1 cosecA-cotA/1 cosecA cotA?
Answer:
To solve the expression 1 cosecA - cotA / 1 cosecA cotA, we can simplify it step by step using trigonometric identities. Let's break down the expression into smaller parts and simplify them individually before combining them.
Step 1: Simplifying the numerator (1 cosecA - cotA)
To simplify the numerator, we will use the trigonometric identity:
cosecA = 1/sinA
cotA = 1/tanA
Substituting these values into the numerator, we get:
1/sinA - 1/tanA
Next, we need to get a common denominator. The common denominator here will be sinA * tanA. So, let's multiply the first term by tanA and the second term by sinA:
(tanA/sinA) - (sinA/tanA)
Simplifying further, we get:
(tan^2A - sin^2A) / (sinA * tanA)
Step 2: Simplifying the denominator (1 cosecA cotA)
To simplify the denominator, we use the following trigonometric identities:
cosecA = 1/sinA
cotA = 1/tanA
Substituting these values into the denominator, we get:
1/sinA * 1/tanA
Multiplying the two fractions, we get:
1/(sinA * tanA)
Step 3: Simplifying the expression
Now that we have simplified the numerator and denominator separately, we can combine them to simplify the expression as a whole.
The expression becomes:
(tan^2A - sin^2A) / (sinA * tanA) divided by 1/(sinA * tanA)
When we divide by a fraction, it is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as:
(tan^2A - sin^2A) / (sinA * tanA) * (sinA * tanA) / 1
Simplifying further, we can cancel out the common terms in the numerator and denominator:
(tan^2A - sin^2A) / 1
Using the trigonometric identity tan^2A - sin^2A = 1, we get:
1 / 1
Therefore, the simplified expression is equal to 1.
In summary, the expression 1 cosecA - cotA / 1 cosecA cotA simplifies to 1.
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1 cosecA-cotA/1 cosecA cotA?
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1 cosecA-cotA/1 cosecA cotA? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 1 cosecA-cotA/1 cosecA cotA? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1 cosecA-cotA/1 cosecA cotA?.
1 cosecA-cotA/1 cosecA cotA? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 1 cosecA-cotA/1 cosecA cotA? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1 cosecA-cotA/1 cosecA cotA?.
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