Simplify tan(20)-(cos(70))/(cos(20))

Problem

tan(20)−cos(70)/cos(20)

Solution

1. Apply cofunction identities to the numerator of the fraction. Since 70 and 20 are complementary angles, use the identity cos(90−θ)=sin(θ)

cos(70)=cos(90−20)=sin(20)

2. Substitute the identity back into the original expression.

tan(20)−sin(20)/cos(20)

3. Apply the tangent identity which states that tan(θ)=sin(θ)/cos(θ)

sin(20)/cos(20)=tan(20)

4. Subtract the two terms to find the final value.

tan(20)−tan(20)=0

Final Answer

tan(20)−cos(70)/cos(20)=0

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