28. 1.8 ००56 +5in0=+2 cos 0. Show that cos 6 — sin 6 = o3 sind 9

1.	28. 1.8 ००56 +5in0=+2 cos 0. Show that cos 6 — sin 6 = o3 sind 9:77 2B
Answer» cosA+sinA=√2cosA squaring both the sides =>(cosA+sinA)²=2cos²A =>cos²A+sin²A+2sinAcosA=2cos²A =>cos²A-2cos²A+2sinAcosA= -sin²A => -cos²A+2sinAcosA= -sin²A => cos²A-2sinAcosA=sin²A adding sin²A on both the sides => cos²A+sin²A-2sinAcosA=2sin²A => (cosA-sinA)²=2sin²A => cosA-sinA=√2sinA Hence proved Like if you find it useful

28. 1.8 ००56 +5in0=+2 cos 0. Show that cos 6 — sin 6 = o3 sind 9:77 2B

Answer»

cosA+sinA=√2cosA

squaring both the sides

=>(cosA+sinA)²=2cos²A

=>cos²A+sin²A+2sinAcosA=2cos²A

=>cos²A-2cos²A+2sinAcosA= -sin²A

=> -cos²A+2sinAcosA= -sin²A

=> cos²A-2sinAcosA=sin²A

adding sin²A on both the sides

=> cos²A+sin²A-2sinAcosA=2sin²A

=> (cosA-sinA)²=2sin²A

=> cosA-sinA=√2sinA

Hence proved

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