√[(1-cos2θ)sec2θ] = tanθ. Write ‘True’ or ‘False’ and justify your answer
Solution:
Given, the expression is √[(1 - cos²θ)sec²θ] = tanθ
We have to determine if the given relation is true or not.
By using trigonometric identities,
cos² A + sin² A = 1
sin² A = 1 - cos² A
So, 1 - cos²θ = sin²θ
Now, √[(1 - cos²θ)sec²θ] = √(sin²θ sec²θ)
= sinθ × secθ
We know that sec A = 1/cos A
= sin θ/cos θ
We know that tan A = sin A/cos A
= tan θ
Therefore, √[(1 - cos²θ)sec²θ] = tanθ
✦ Try This: √[(1 - sin²θ)cosec²θ] = cotθ
Given, √[(1 - sin²θ)cosec²θ] = cotθ
We have to determine if the given relation is true or not.
By using trigonometric identity,
cos² A = 1 - sin² A
√[(1 - sin²θ)cosec²θ] = √(cos²θcosec²θ)
= cosθ × cosecθ
We know cosec A = 1/sin A
= cosθ/sinθ
We know that cot A = cos A/sin A
= cotθ
Therefore, √[(1 - sin²θ)cosec²θ] = cotθ
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 4
√[(1-cos2θ)sec2θ] = tanθ. Write ‘True’ or ‘False’ and justify your answer
Summary:
Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain.The statement “√[(1-cos²θ)sec²θ] = tanθ” is true
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