Verify the identity , justify each step
tanØ+cotØ = 1/ sin Ø cosØ
use the identities
tanφ=sinφ/cosφ
cotφ=cosφ/sinφ
sin²φ+cos²φ=1
tanφ+cotφ
=sinφ/cosφ+cosφ/sinφ
=(sin²φ+cos²φ)/(sinφcosφ)
=1/(sinφcosφ)
Thanks you
You're welcome!
To verify the given identity tanØ + cotØ = 1/ sinØ cosØ, we need to manipulate the left-hand side (LHS) of the equation and simplify it until it matches the right-hand side (RHS) of the equation. Here's how we can do it step by step:
Step 1: Start with the LHS of the equation: tanØ + cotØ.
Step 2: Rewrite cotØ as 1/tanØ. The LHS now becomes tanØ + 1/tanØ.
Step 3: To combine the fractions, find a common denominator. The common denominator is tanØ, so we multiply the second term (1/tanØ) by tanØ/tanØ, which yields tanØ + tanØ/tanØ.
Step 4: Combine the fractions over a common denominator, which is tanØ in this case. The LHS now becomes (tanØ * tanØ + tanØ)/tanØ.
Step 5: Simplify the numerator by factoring out the common factor of tanØ. This gives us tanØ(tanØ + 1)/tanØ.
Step 6: Cancel out the common factor of tanØ from the numerator and denominator. We are left with tanØ + 1 as our final expression.
Step 7: Compare the simplified expression with the RHS of the equation (1/ sin Ø cosØ). We can see that tanØ + 1 = 1/ sin Ø cosØ.
Since the LHS of the equation simplifies to the same expression as the RHS, we have verified the given identity.