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physics kiddy
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Homework Statement
Prove that:
tan^2∅/tan∅ - 1 + cot^2∅/cot∅ - 1 = 1 + sec∅cosec∅
Homework Equations
The Attempt at a Solution
I have solved the question taking tan∅ = sin∅/cos∅.
But I want to solve it some other way.
What you wrote for the left hand side is literally (tan^2∅/tan∅) - 1 + (cot^2∅/cot∅) - 1, which is equivalent to tan∅ + cot∅ - 2 .physics kiddy said:Homework Statement
Prove that:
tan^2∅/tan∅ - 1 + cot^2∅/cot∅ - 1 = 1 + sec∅cosec∅
Homework Equations
The Attempt at a Solution
I have solved the question taking tan∅ = sin∅/cos∅.
But I want to solve it some other way.
What is the angle(acute) between two lines of slopes say, m1 and m2?physics kiddy said:Thanks, I got the answer. But I have got one more question:
How to prove that slopes of perpendicular lines on graph paper have a product equal to -1 ?
A trigonometric identity is an equation involving trigonometric functions that is true for all values of the variables involved. These identities are important in solving trigonometry problems and simplifying expressions.
Some common trigonometric identities include the Pythagorean identities, double angle identities, half angle identities, and sum and difference identities. These identities can be used to simplify trigonometric expressions and solve equations.
Trigonometric identities can be proved using algebraic manipulation and substitution of known identities. Another method is to use geometric proofs, where the identities are proven based on the relationships between angles and sides of triangles.
Trigonometric identities are important in mathematics because they allow for the simplification of complex trigonometric expressions, making them easier to solve. These identities are also used in many fields such as physics, engineering, and navigation.
Trigonometric identities have many real-life applications, including calculating distances and heights using angles and sides of triangles, analyzing sound and light waves, and predicting the movement of objects in circular motion such as planets and satellites.