In triangle ABC, angle C is right angle. AB =29, BC =21 then value cos²B + sin²B. About the author Kennedy
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 . Reply
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
.