How do you simplify the expression #tan^2xcsc^2x-tan^2x#?
The expression simplifies to
I hope this is useful!
By signing up, you agree to our Terms of Service and Privacy Policy
To simplify the expression (\tan^2x\csc^2x - \tan^2x), you can factor out the common term (\tan^2x).
[ \tan^2x(\csc^2x - 1) ]
Recall that (\csc^2x - 1) can be simplified using the Pythagorean identity for cosecant:
[ \csc^2x - 1 = \cot^2x ]
So the expression becomes:
[ \tan^2x(\cot^2x) ]
Now, using the fact that (\tan x = \frac{1}{\cot x}) and squaring both sides, we get:
[ \tan^2x = \frac{1}{\cot^2x} ]
So, we can rewrite the expression as:
[ \frac{1}{\cot^2x} \cdot \cot^2x = 1 ]
Therefore, the simplified expression is (1).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- Use double-angle or half-angle formula to simplify #(2-csc^2(x))/(csc^2(x))# ?
- How do you find tan alpha = -15/8, with alpha in quadrant II?
- How do you solve #Sin45 = 12/x #?
- How do you verify # (sin(theta)+cos(theta))^(2) + (sin(theta)-cos(theta))^(2)=2#?
- How do you use double angle identity for sin 2x given that cos x= 4/5 where x is an angle in quadrant 1?
![Answer Background](/cdn/public/images/tutorgpt/ai-tutor/answer-ad-bg.png)
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7