If cos4x.sec2y,12,sin4x.csc2y are in A.P, then prove that cos8x.sec6y,12,sin8x.csc6y in A.P My Attempt cos4x.sec2y+sin4.xcsc2y=cos4xcos2y+sin4xsin2y=1 ⇒sin2y.cos4x+cos2y.sin4x=sin2y.cos2y...

Fiona Petersen

Fiona Petersen

Answered

2022-01-26

If cos4x.sec2y,12,sin4x.csc2y are in A.P, then prove that cos8x.sec6y,12,sin8x.csc6y in A.P
My Attempt
cos4x.sec2y+sin4.xcsc2y=cos4xcos2y+sin4xsin2y=1
sin2y.cos4x+cos2y.sin4x=sin2y.cos2y
cos8x.sec6y+sin8x.csc6y=cos8xcos6y+sin8xsin6y
How do I know that the given terms are in A.P, G.P or H.P ?

Answer & Explanation

Karli Kaiser

Karli Kaiser

Expert

2022-01-27Added 9 answers

Hint:
12cos4x=2(sin4x12)
2(1+cos2x)2=2(1cos2x)24
Solve for cos2x
csc2y12=2(12sec2y)
24(1+tan2y)=2(1+cot2y)1
4tan2y+21tan2y5=0
Solve for tan2y0

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