Question

show that cos square a minus sin square is equal to 2 cos square a minus one​

Answer 1

show that cos square a minus sin square is equal to 2 cos square a minus one

Answer 2

To show

We have to show that cos²a-sin²a=2cos²-1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

How to solve :

We will solve with the help of trigonometric Identities.We have to see that what's the question demand e.g.,here we have to show 2cos²-1 and in Question also cos²a as well as sin²a so,we have to convert sin into cos for this we use this identity:

➙Sin²a+cos²a=1

➙cos²a-sin²a

sin²a= 1-cos²a--(1)

from equation 1

➙cos²-(1-cos²a)

➙cos²a-1+cos²a

➙2cos²a-1

Hence, proved LHS=RHS

More trigonometric identities

• sin²Θ+cos²Θ=1
• sec²Θ=1+tan²Θ
• cosec²Θ=1+cot²Θ

Reciprocal identities

• Sinθ= 1/cosecθ
• cosθ=1/secθ
• tanθ=1/cotθ

Angle formulas

• sin(90°−θ) = cos θ
• cos(90°−θ) = sin θ
• tan(90°−θ) = cot θ
• cot(90°−θ) = tan θ
• sec(90°−θ) = cosec θ
• cosec(90°−θ) = sec θ