Question 17: Find the values of tan¯¹ (tan 3π/4)
Class 12 - Math - Inverse Trigonometric Functions
Answers
Answered by
12
3pi/4 can be written as pi+pi/4
And pi+pi/4 comes in third quadrant where tanx is positive.
So above eqn. Becomes tan inverse (tan pi/4)
Which is equal to pi/4.
As tan inverse(tanx) is x under its principle values.
Hope you get your answer.
And pi+pi/4 comes in third quadrant where tanx is positive.
So above eqn. Becomes tan inverse (tan pi/4)
Which is equal to pi/4.
As tan inverse(tanx) is x under its principle values.
Hope you get your answer.
Answered by
46
tan-¹(tan3π/4)
we know that tan-¹(tanx) = x if x€(-π/2,π/2)
Therefore tan-¹(tan3π/4)
= tan-¹(tan(π-π/4)) = tan-¹(-tanπ/4)
= -π/4 € (-π/2,π/2)
hence tan-¹(tan3π/4) = -π/4
we know that tan-¹(tanx) = x if x€(-π/2,π/2)
Therefore tan-¹(tan3π/4)
= tan-¹(tan(π-π/4)) = tan-¹(-tanπ/4)
= -π/4 € (-π/2,π/2)
hence tan-¹(tan3π/4) = -π/4
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