Solving Trigonometric Identities Online
An equation is an equality which is true only for several values of the variable
. An expression can be given more clear and convenient form by an identity.Solving Trigonometric Identities Online:
Online trigonometric identities solving shows a clear idea about a tutor solves a problem in online. Some of the trigonometric identities and example problems using trigonometric identities are listed below.
Types of Trigonometric Identities:
There are several identities in trigonometry. Here we see some of trignometric identities online. They are as follows,
Reciprocal identities,
sin x = '1 / csc x' , csc x = '1 / sin x' ,
cos x = '1 / sec x' , sec x = '1 / cos x' ,
tan x = '1 / cot x' , cot x = '1 / tan x' .
Tangent and Cotangent identities,
tan x = 'sin x / cos x' ,
cot x = 'cos x / sin x' .
Pythagorean identities,
sin2x + cos2x = 1,
1 + tan2x = sec2x,
1 + cot2x = csc2x.
Co-function identities,
sin (90 x) = cos x, cos (90 x) = sin x, tan (90 x) = cot x,
csc (90 x) = sec x, sec (90 x) = csc x, cot (90 x) = tan x.
Even-Odd identities,
sin (x) = sin x, cos (x) = cos x, tan (x) = tan x,
csc (x) = csc x, sec (x) = sec x, cot (x) = cot x.
Examples of Solving Trigonometric Identities Online:
Ex 1: Solve sin30 by using cos60 = 0.5
Sol : Solving sin 30,
sin30 = sin(90 60)
= cos60 [Using Co-Function Identity]
= 0.5
Therefore, sin30 = 0.5
Ex 2: Prove that, sec2x + csc2x = sec2x csc2x using trigonometric identities.
Proof:
Solving L.H.S. ,
L.H.S. = sec2x + csc2x
= ('1 / (cos^(2)x)' ) + ('1 / (sin^(2)x)' ) [Using Reciprocal Identity]
= ' (sin^(2)x + cos^(2)x) / (sin^(2)x cos^(2)x)' [Taking L.C.M. ]
= '1 / (sin^(2)x cos^(2)x)' [Using Pythagorean Identity]
= '1 / (sin^(2)x)' '1 / (cos^(2)x)' [Separating it Into Two Terms]
= csc2x sec2x [Using Reciprocal Identity]
= sec2x csc2x
= R.H.S.
Hence, proved that sec2x + csc2x = sec2x csc2x.
Ex 3:
Prove that, sin4 a 2sin2 a cos2 a + cos4 a = cos2 (2 a), Using Trigonometric Functions calculus.
Proof:
L.H.S. = sin4 a 2 sin2 a cos2 a + cos4 a
= (sin2 a)2 2sin2 a cos2 a + (cos2 a)2
= (sin2 a cos2 a)2 [ Using ( a b )2 = a2 2ab + b2 ]
= ((1 cos2 a) cos2 a)2 [By Pythagorean identity ]
= (1 2cos2 a)2
=( (2cos2 a 1))2
=( cos 2a)2 [ Using Formula: cos 2 = 2 cos2 1 ]
=cos2 (2 a)
= R.H.S.
Hence proved that, sin4 a 2sin2 a cos2 a + cos4 a = cos2 (2 a).
by: Smith Earn Money Writing Online Without Having Any Earlier Past Experiences Save Money On Purchases With Voucher Codes From Money-off Websites Online What To Consider Before Buying A Dell Inspiron 1520 Battery Online? Tips On Finding Best Car Leasing Deal Online Benefits Of Online Taxi Reservation How To Learn English Using English Courses Online Designer Clothes Online For Babies Are You Familiar With This Concept? Find List Of Apartments For Sale Online In Bhopal Get Original Art At Fine Art Photography Online Gallery Why Go The Hard Way For Packaging Supplies When You Have Online Sources Readily? Honeymoon Decoration Ideas With Online Flowers Dodge Charger Accessories Choose Your Preferred Part Online Why Online Gift Stores Are Most Popular