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The sum formula of tangent function is, tan (A + B) = (tan A + tan B) / (1 – tan A tan B) When A = B, the above formula becomes, tan (A + A) = (tan A + tan A) / (1 – tan A tan A) =(2 tan A) / (1 – tan2A)…

The sum formula of cosine function is, cos (A + B) = cos A cos B – sin A sin B When A = B, the above formula becomes, cos (A + A) = cos A cos A – sin A sin A cos 2A = cos2A – sin2A Let us use this as a…

The sum formula of sine function is, sin (A + B) = sin A cos B + cos A sin B When A = B, the above formula becomes, sin (A + A) = sin A cos A + cos A sin A sin 2A = 2 sin A cos A Let us derive an alternate…

sin(x+y) = sin(x)cos(y)+cos(x)sin(y) cos(x+y) = cos(x)cos(y)–sin(x)sin(y) t a n ( x + y ) = t a n   x + t a n   y / 1 − t a n   x . t a n   y sin(x–y) = sin(x)cos(y)–cos(x)sin(y) cos(x–y) = cos(x)cos(y) + sin(x)sin(y) t a n ( x − y ) = t a n   x − t a…

The co-function or periodic identities can also be represented in degrees as: sin(90°−x) = cos x cos(90°−x) = sin x tan(90°−x) = cot x cot(90°−x) = tan x sec(90°−x) = cosec x cosec(90°−x) = sec x

These formulas are used to shift the angles by π/2, π, 2π, etc. They are also called co-function identities. sin (π/2 – A) = cos A & cos (π/2 – A) = sin A sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A sin (3π/2 – A)  =…

Below is the table for trigonometry formulas for angles that are commonly used for solving problems. Angles (In Degrees) 0° 30° 45° 60° 90° 180° 270° 360° Angles (In Radians) 0 π/6 π/4 π/3 π/2 π 3π/2 2π sin 0 1/2 1/√2 √3/2 1 0 -1 0 cos 1 √3/2 1/√2 1/2 0 -1 0…

The Reciprocal Identities are given as: cosec θ = 1/sin θ sec θ = 1/cos θ cot θ = 1/tan θ sin θ = 1/cosec θ cos θ = 1/sec θ tan θ = 1/cot θ All these are taken from a right-angled triangle. When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are also derived by using the…

There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent. By using a right-angled triangle as a reference, the trigonometric functions and identities are derived: sin θ = Opposite Side/Hypotenuse cos θ = Adjacent Side/Hypotenuse tan θ = Opposite Side/Adjacent Side sec…