cos² (0+45°) + cos² (0-45°) = 1
Answers
Step-by-step explanation:
To find cos245o−sin215o
We know that, cos2θ=2cos2θ−1⟹cos2θ=21+cos2θ
And cos2θ=1−2sin2θ⟹sin2θ=21−cos2θ
∴cos245o=21+cos(2×45)=21+cos90o=21+0=21
Also, ∴sin215o=21−cos(2×15)=21−cos30o=21−23
To find cos
2
45
o
−sin
2
15
o
o
o We know that, cos2θ=2cos
2
θ−1⟹cos
2
θ=
2
1+cos2θ
1+cos2θ
1+cos2θ
1+cos2θ And cos2θ=1−2sin
2
θ⟹sin
2
θ=
2
1−cos2θ
1−cos2θ
1−cos2θ
1−cos2θ ∴cos
2
45
o
= 2
1+cos(2×45)
1+cos(2×45)
= 2
1+cos90
o
o
o
= 2
1+0
1+0
= 2
1
1
1
1 Also, ∴sin 2
1 Also, ∴sin 2 15
o
o =
o = 2
o = 21−cos(2×15)
o = 21−cos(2×15)
o = 21−cos(2×15) =
o = 21−cos(2×15) = 2
o = 21−cos(2×15) = 21−cos30
o = 21−cos(2×15) = 21−cos30 o
o = 21−cos(2×15) = 21−cos30 o
o = 21−cos(2×15) = 21−cos30 o
o = 21−cos(2×15) = 21−cos30 o =
o = 21−cos(2×15) = 21−cos30 o = 2
o = 21−cos(2×15) = 21−cos30 o = 21−
o = 21−cos(2×15) = 21−cos30 o = 21− 2
o = 21−cos(2×15) = 21−cos30 o = 21− 23
o = 21−cos(2×15) = 21−cos30 o = 21− 23
o = 21−cos(2×15) = 21−cos30 o = 21− 23
o = 21−cos(2×15) = 21−cos30 o = 21− 23
o = 21−cos(2×15) = 21−cos30 o = 21− 23
o = 21−cos(2×15) = 21−cos30 o = 21− 23
o = 21−cos(2×15) = 21−cos30 o = 21− 23 =
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 2
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 −
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 4
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o =
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 2
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 −
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 2
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 +
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 4
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43 =
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43 = 4
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43 = 43
o = 21−cos(2×15) = 21−cos30 o = 21− 23 = 21 − 43 Then we get,cos 2 45 o −sin 2 15 o = 21 − 21 + 43 = 43
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