(secx)/(tanx)+(cscx)/(cotx)=secx+cscx

Please help me verify this trigonometric identity.

change all to sine, cosine on the left.

You get 1/cosx+ 1/sinx which is secx+cscx

To verify the given trigonometric identity, we need to simplify both sides of the equation and show that they are equal.

Let's start with the left side of the equation and simplify it step by step:

(secx)/(tanx) + (cscx)/(cotx)

To simplify this, we need to recall the trigonometric identities:

1. secx = 1/cosx
2. tanx = sinx/cosx
3. cscx = 1/sinx
4. cotx = cosx/sinx

Now, substituting these identities into our equation, we have:

(1/cosx)/(sinx/cosx) + (1/sinx)/(cosx/sinx)

Next, we can simplify it further by multiplying the numerator and denominator of the fractions:

(1/cosx) * (cosx/sinx) + (1/sinx) * (sinx/cosx)

The cosx in the numerator and the sinx in the denominator cancel out:

1/sinx + 1/cosx

Now, to combine the two fractions, we need to find the least common denominator (LCD), which is sinx * cosx:

(cosx + sinx) / (sinx * cosx)

Now, let's simplify the right side of the equation of the given identity, which is secx + cscx:

Using the same trigonometric identities as above and substituting them into the equation, we have:

1/cosx + 1/sinx

To combine the fractions, we need to find the LCD, which is sinx * cosx:

(sinx + cosx) / (sinx * cosx)

Now, we can see that the left side of the equation (cosx + sinx) / (sinx * cosx) is equal to the right side of the equation (sinx + cosx) / (sinx * cosx).

Therefore, we have verified that the trigonometric identity (secx)/(tanx) + (cscx)/(cotx) = secx + cscx is true.