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If sin inverse x plus cos inverse x is p then the value of 2tanp/3divided by 1 minus tan square p/3?
Most Upvoted Answer
If sin inverse x plus cos inverse x is p then the value of 2tanp/3divi...
Explanation:
We are given that:
sin inverse x + cos inverse x = p
To solve the given expression, we need to use the following trigonometric identities:
- sin (a + b) = sin a cos b + cos a sin b
- cos (a + b) = cos a cos b – sin a sin b
- tan (a + b) = (tan a + tan b) / (1 – tan a tan b)
- sin^2 a + cos^2 a = 1
Solution:
Let us begin by using the first two identities to find sin p and cos p:
sin p = sin (sin inverse x + cos inverse x)
= sin inverse x cos cos inverse x + cos inverse x sin sin inverse x
= x sqrt(1 – x^2) + sqrt(1 – x^2) x
= sqrt(1 – x^2) (x + 1)
cos p = cos (sin inverse x + cos inverse x)
= cos inverse x cos sin inverse x – sin inverse x sin cos inverse x
= sqrt(1 – x^2) sqrt(1 – x^2) – x x
= 1 – 2x^2
Now, we can use these values to find tan p:
tan p = sin p / cos p
= (x + 1) / (1 – 2x^2)
Next, we can use the third identity to find 2tanp/3:
2tanp/3 = 2tan (p/3 + p/3)
= 2(tan p/3 + tan p/3 / (1 – tan^2 p/3)
= 2[(tan p/3 + tan p/3) / (1 – tan^2 p/3)]
= 2[2tan p/3 / (1 – tan^2 p/3)]
= 4tan p/3 / (1 – tan^2 p/3)
Finally, we can substitute the value of tan p to get:
2tanp/3 / (1 – tan^2 p/3) = 4[(x + 1) / (1 – 2x^2)] / [1 – (x + 1)^2 / (1 – 2x^2)]
= 4(x + 1) / (1 – 3x^2)
Hence, the value of 2tanp/3 / (1 – tan^2 p/3) is 4(x + 1) / (1 – 3x^2).
Community Answer
If sin inverse x plus cos inverse x is p then the value of 2tanp/3divi...
We know that sin inverse x+ cos inverse x=pie/2
(from properties)
Here, given sin inverse x + cos inverse x = p
hence,p=pie/2
now, (2tanp/3)/(1- tan^2p/3)=?
put pie/2 in place of p
so we will get, (2tan pie/6)/(1-tan^2 pie/6)
tan pie/6=1/√3
=(2/√3)/(1- 1/3)
=(2/√3)/(2/3)
=√3
(from properties)
Here, given sin inverse x + cos inverse x = p
hence,p=pie/2
now, (2tanp/3)/(1- tan^2p/3)=?
put pie/2 in place of p
so we will get, (2tan pie/6)/(1-tan^2 pie/6)
tan pie/6=1/√3
=(2/√3)/(1- 1/3)
=(2/√3)/(2/3)
=√3
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If sin inverse x plus cos inverse x is p then the value of 2tanp/3divided by 1 minus tan square p/3?
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If sin inverse x plus cos inverse x is p then the value of 2tanp/3divided by 1 minus tan square p/3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If sin inverse x plus cos inverse x is p then the value of 2tanp/3divided by 1 minus tan square p/3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sin inverse x plus cos inverse x is p then the value of 2tanp/3divided by 1 minus tan square p/3?.
If sin inverse x plus cos inverse x is p then the value of 2tanp/3divided by 1 minus tan square p/3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If sin inverse x plus cos inverse x is p then the value of 2tanp/3divided by 1 minus tan square p/3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sin inverse x plus cos inverse x is p then the value of 2tanp/3divided by 1 minus tan square p/3?.
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