Online trig identities examples tutor
Introduction :
Trigonometric identities are nothing but the equalities in which it contain trigonometric functions and are right for every value for all variables .In this topic we shall learn online trigonometry identities with the online of tutor.
Online tutor is the way of learning through internet in which the tutor provides step by step solution to example problems. Students can understand the concepts and prepare well for exam. This article is mainly used for the students who are all using online
Tutor notes on trig identities:
Examples for trigonometry identities:
example 1:
Solve The, cos4N − sin4N = 1 − 2 sin2N.
Online Tutor Solution:
Given that, cos4N − sin4N = 1 − 2 sin2N.
L.H.S. = cos4N − sin4N,
Now we used a2 − b2 = (a + b) (a − b), we get,
=> (cos2N + sin2N) (cos2N − sin2N),
We used cos2N + sin2N = 1, we get,
=> (1) (1 − sin2N − sin2N),
=> 1 − 2sin2N.
=> R.H.S.
Example 2:
Solving trigonometric identities that sin4H − cos4H= sin2H − cos2H
Solution:
LHS = sin4H− cos4H
= (sin2H) 2 – (cos2H) 2
= (sin2H + cos2H) (sin2 H − cos2H)
= (1) (sin2H − cos2H)
= sin2H − cos2H = RHS
Example 3:
Simplify for using trigonometry identities: sin W cos W tan W = 1 − cos2 W
Solution:
LHS = sin W cos W tan W
= sin W cos W` (sin W/cos w)`
= sin2W
= 1-cos2W (Since sin2 W +cos 2W =1)
= RHS
Example 4:
Simplify that sin R+ sin R cot2 R = csc R
solution:
LHS =sin R + sin R cot2R
= sin R (1+cot2R)
=sin R(csc2R)
= sin R`(1/(sin^2R))`
=`1/sinR`
= csc R
=RHS
Example 5:
Simplify that tan Z + cot Z = sec Z csc Z
Solution:
LHS = tan Z +cot Z
= `(sinZ/cosZ)+(cosZ/sinZ)`
=`(sin^2Z+cos^2Z)/(cosZsinZ)`
=`1/(cosZsinZ)`
= sec Z x csc Z
= RHS
Example 6:
Prove the following identity: tan(p)cos(p) = sin(p)
Solution:
tan(p)cos(p) = sin(p)
`(sin p/cos p)` cos p= sin(p)
sin(p) = sin(p)
Trigonometric identities are nothing but the equalities in which it contain trigonometric functions and are right for every value for all variables .In this topic we shall learn online trigonometry identities with the online of tutor.
Online tutor is the way of learning through internet in which the tutor provides step by step solution to example problems. Students can understand the concepts and prepare well for exam. This article is mainly used for the students who are all using online
Tutor notes on trig identities:
- sin a =`1/csc a`
- cos a =` 1/sec a`
- tan a = `1/cot a`
- sin2a+ cos2 a≡ 1
- 1 + tan2a≡ sec2 a
- 1 + cot2a ≡ cosec2 a
- sin2a≡ 1 – cos2a
- cos2a≡ 1 – sin2a
- tan2a ≡ sec2a − 1
- sec2a − tan2a ≡ 1
- cot2a ≡ cosec2a − 1
- cosec2a − cot2a ≡ 1
Examples for trigonometry identities:
example 1:
Solve The, cos4N − sin4N = 1 − 2 sin2N.
Online Tutor Solution:
Given that, cos4N − sin4N = 1 − 2 sin2N.
L.H.S. = cos4N − sin4N,
Now we used a2 − b2 = (a + b) (a − b), we get,
=> (cos2N + sin2N) (cos2N − sin2N),
We used cos2N + sin2N = 1, we get,
=> (1) (1 − sin2N − sin2N),
=> 1 − 2sin2N.
=> R.H.S.
Example 2:
Solving trigonometric identities that sin4H − cos4H= sin2H − cos2H
Solution:
LHS = sin4H− cos4H
= (sin2H) 2 – (cos2H) 2
= (sin2H + cos2H) (sin2 H − cos2H)
= (1) (sin2H − cos2H)
= sin2H − cos2H = RHS
Example 3:
Simplify for using trigonometry identities: sin W cos W tan W = 1 − cos2 W
Solution:
LHS = sin W cos W tan W
= sin W cos W` (sin W/cos w)`
= sin2W
= 1-cos2W (Since sin2 W +cos 2W =1)
= RHS
Example 4:
Simplify that sin R+ sin R cot2 R = csc R
solution:
LHS =sin R + sin R cot2R
= sin R (1+cot2R)
=sin R(csc2R)
= sin R`(1/(sin^2R))`
=`1/sinR`
= csc R
=RHS
Example 5:
Simplify that tan Z + cot Z = sec Z csc Z
Solution:
LHS = tan Z +cot Z
= `(sinZ/cosZ)+(cosZ/sinZ)`
=`(sin^2Z+cos^2Z)/(cosZsinZ)`
=`1/(cosZsinZ)`
= sec Z x csc Z
= RHS
Example 6:
Prove the following identity: tan(p)cos(p) = sin(p)
Solution:
tan(p)cos(p) = sin(p)
`(sin p/cos p)` cos p= sin(p)
sin(p) = sin(p)