show that cos^2 45-sin^2 15=√3/4.
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L.H.S.=Cos^2(45°) - Sin^2(15°)
={Cos(45°)}^2 - [Sin (45°-30°)]^2
={Cos(45°)}^2 - [Sin45°×Cos30°-Cos45°×Sin30°]^2
=(1/√2)^2 - [(1/√2 ×√3/2) - (1/√2×1/2)]^2
=1/2 - [√3/2√2 - 1/2√2]^2
=1/2 - (√3–1/2√2)^2
=1/2 - [(√3–1)^2/4×2]
=1/2 - [(√3)^2-2×√3×1+(1)^2/8]
=1/2 - [3–2√3+1/8]
=1/2 - 4+2√3/8
=4–4+2√3/8
=2√3/8
=√3/4
= R.H.S
Hence proved
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