Evaluate 1+tan(30 degrees )^2-csc(45 degrees )^2

Problem

1+tan2(30)−csc2(45)

Solution

1. Identify the trigonometric values for the given angles.

tan(30)=1/√(,3)

csc(45)=√(,2)

2. Substitute these values into the expression.

1+(1/√(,3))2−(√(,2))2

3. Evaluate the squares of the trigonometric values.

(1/√(,3))2=1/3

(√(,2))2=2

4. Simplify the expression by performing the addition and subtraction.

1+1/3−2

4/3−2

4/3−6/3

−2/3

Final Answer

1+tan2(30)−csc2(45)=−2/3

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