Explanation
Using,
tanx=cot(90∘−x) and tanx.cotx=1
We get ,
tan5.tan10.tan15...tan80.tan85=tan5.tan10.tan15...tan45.cot(90−35)...cot(90−10).cot(90−5)=tan5.cot5.tan10.cot10...tan45=1
In △ABC, BC=15, sinB=45 Now, sinB=PH 45=ACAB Then, let AC=4x and AB=5x Now, AB2=AC2+BC2 (5x)2=(4x)2+152 25x2=16x2+225 9x2=225 x=5 Hence, AC=20 and AB=25 tan∠ADC=1 ACCD=1 AC=CD=20 Now, using Pythagoras theorem, AD2=AC2+CD2 AD2=202+202 AD=20√2
In △ABC, BC=15, sinB=45 Now, sinB=PH 45=ACAB Then, let AC=4x and AB=5x Now, AB2=AC2+BC2 (5x)2=(4x)2+152 25x2=16x2+225 9x2=225 x=5 Hence, AC=20 and AB=25
sinx+sin2x+sin3x=1⇒sinx+sin3x=1−sin2x⇒sinx(1+sin2x)=cos2x⇒sinx(2−cos2x)=cos2x⇒sin2x(2−cos2x)2=cos4x⇒(1−cos2x)(4+cos4x−4cos2x)=cos4x⇒4+cos4x−4cos2x−4cos2x−cos6x+4cos4x=cos4x⇒cos6x−4cos4x+8cos2x=4
Please disable the adBlock and continue. Thank you.