1)tan 5 degrees + tan 25 degrees / 1 tan 5 degrees tan 25 degrees =

sqrt 3 / 3 Am I correct?

2) Complete the identity

tan^2Q - 3sinQtanQsecQ =

-2tan^2Q Correct?

You are correct if your expression is

(tan5 + tan25)/(1 - tan5tan25), which is not what you typed.

yes, to your second part

(tan5 + tan25)/(1 - tan5tan25)= tan (5+25) = tan 30 degrees = (sqrt 3)/3

1) To solve the expression tan 5 degrees + tan 25 degrees / (1 - tan 5 degrees tan 25 degrees), we can follow these steps:

Step 1: Calculate the values of tan 5 degrees and tan 25 degrees:
You can use a scientific calculator or an online calculator to find the exact values of tangent for 5 degrees and 25 degrees. For example, tan 5 degrees is approximately 0.087 and tan 25 degrees is approximately 0.466.

Step 2: Substitute these values in the expression:
tan 5 degrees + tan 25 degrees / (1 - tan 5 degrees tan 25 degrees)
= 0.087 + 0.466 / (1 - 0.087 * 0.466)

Step 3: Solve the expression:
Now, perform the multiplication and division first, following the order of operations (PEMDAS or BODMAS):
= 0.087 + 0.466 / (1 - 0.087 * 0.466)
= 0.087 + 0.466 / (1 - 0.040362)
= 0.087 + 0.466 / 0.959638
= 0.087 + 0.485

Step 4: Simplify further:
= 0.572

So, the final answer is 0.572, which is not equal to sqrt(3)/3. Therefore, your answer is incorrect.

2) To complete the identity tan^2Q - 3sinQtanQsecQ = -2tan^2Q, we can follow these steps:

Step 1: Recall the trigonometric identity:
tan^2Q - 3sinQtanQsecQ

Step 2: Simplify using known trigonometric identities:
We know that secQ = 1/cosQ, so secQ = 1/cosQ = 1/(√(1 - sin^2Q)).
Using this, we can rewrite the given expression as:
tan^2Q - 3sinQtanQ(1/(√(1 - sin^2Q)))

Step 3: Multiply further:
= tan^2Q - 3sinQtanQ/√(1 - sin^2Q)

Step 4: Recall the identity tanQ = sinQ/cosQ:
= (sinQ/cosQ)^2 - 3sinQ(sinQ/cosQ)/√(1 - sin^2Q)

Step 5: Simplify using the identity sin^2Q = 1 - cos^2Q:
= (sin^2Q/cos^2Q) - 3sinQ(sinQ/cosQ)/√(1 - (1 - cos^2Q))

Step 6: Further simplify:
= (sin^2Q/cos^2Q) - 3sin^2Q/cosQ√(cos^2Q)
= (sin^2Q - 3sin^2Q)/cos^2Q√(cos^2Q)
= -2sin^2Q/cos^2Q√(cos^2Q)

Step 7: Simplify further:
= -2sin^2Q/√(cos^2Q)

Step 8: Recall the identity sin^2Q = 1 - cos^2Q:
= -2(1 - cos^2Q)/√(cos^2Q)
= -2 + 2cos^2Q/√(cos^2Q)

Step 9: Simplify and write in terms of tangent:
= -2 + 2cos^2Q/cosQ
= -2 + 2cosQ

So, the completed identity is tan^2Q - 3sinQtanQsecQ = -2tan^2Q = -2 + 2cosQ. Therefore, your answer is correct.