In triangle ABC, angle C is right angle. AB =29, BC =21 then value cos²B + sin²B.​

Question

In triangle ABC, angle C is right angle. AB =29, BC =21 then value cos²B + sin²B.​

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Kennedy 1 month 2021-08-16T07:16:59+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-16T07:18:20+00:00

    Answers:

    By Pythagoras theorem,

    AB

    2

    =AC

    2

    +BC

    2

    ⇒AC

    2

    =AB

    2

    −BC

    2

    ⇒AC

    2

    =29

    2

    −21

    2

    =(29+21)(29−21)=50×8

    ⇒AC

    2

    =25×16

    ⇒AC=5×4=20 units

    ⇒cosθ=

    AB

    BC

    =

    29

    21

    ,

    sinθ=

    AB

    AC

    =

    29

    20

    ⇒sin2θ+cos

    2

    θ=

    29

    2

    21

    2

    +20

    2

    =

    29

    2

    29

    2

    =1

    ⇒cos

    2

    θ−sin

    2

    θ=

    29

    2

    21

    2

    −20

    2

    =

    841

    41

    .

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