Establish identity:
tan theta + cot theta
-------------------- equal to(=) csc²theta
tan theta
Can you draw the ans. bec. I cant understand which they are aligned.
To establish the identity:
1. Start with the left side of the equation: tan(theta) + cot(theta) / tan(theta)
2. Since cot(theta) is the reciprocal of tan(theta), substitute cot(theta) with 1/tan(theta): tan(theta) + (1/tan(theta)) / tan(theta)
3. Combine the fractions: (tan(theta) * tan(theta) + 1) / tan(theta)
4. Simplify the numerator: (tan²(theta) + 1) / tan(theta)
5. Recall the Pythagorean Identity: tan²(theta) + 1 = sec²(theta)
6. Substitute the numerator with sec²(theta): sec²(theta) / tan(theta)
7. Finally, recall the reciprocal identity: csc(theta) = 1/sin(theta)
8. Substitute sec(theta) with 1/cos(theta), and tan(theta) with sin(theta)/cos(theta): (1/cos²(theta)) / (sin(theta)/cos(theta))
9. Simplify by multiplying the numerator by the reciprocal of the denominator: (1/cos²(theta)) * (cos(theta)/sin(theta))
10. Cancel out the common terms: 1/sin(theta)
11. Rewrite the reciprocal identity: csc(theta)
Therefore, the left side of the equation simplifies to csc²(theta), which is equal to the right side of the equation.
As for drawing the solution, mathematical equations are typically represented using symbols and equations rather than visual drawings.