Trigonometry-class 8

Opt Maths solution:

Class – 8

1.    Find the product of the following:

       i.            (1+sinq)(1-sinq)

    ii.            (tanA+cotA)(tanA-cotA)

 iii.            (sina+cosa)(sina-cosa)

 iv.            (3secβ-2secβ)(3secβ-2secβ)

    v.            (1+tanA)(1-tanA)(1+tan²A)

 vi.         (sinq-cosq)(sin²q+sinq.cosq+cos²q)

Solution of questions:

       i.            Solution: here,

L.H.S=(1+sinq)(1-sinq)

          =(1-sin²q)

          =R.H.S

          Hence proved

    ii.            Solution: here,

L.H.S=(tanA+cotA)(tanA-cotA)

=(tan²A-cot²A)

=R.H.S

Hence proved

 iii.            Solution: here,

L.H.S=(sina+cosa)(sina-cosa)

          =(sin²a-cos²a)

          =R.H.S

          Hence proved

 iv.            Solution: here,

L.H.S=(3secβ-2secβ)(3secβ+2secβ)

          =(3sec²β-2sec²β)

          =R.H.S

          Hence proved

    v.            Solution: here,

L.H.S=(1+tanA)(1-tanA)(1+tan²A)

          =(1-tan²A)(1+tan²A)

          =(1-tan⁴A)

          =R.H.S

          Hence proved

 vi.            Solution: here,

L.H.S=(sinq-cosq)(sin²q+sinq.cosq+cos²q)

          =(sin³q-cos³q)

          =R.H.S

          Hence proved