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Prove that: log sin 8x = 3 log2+log sin x+ log cos 2x+log cos 4x

Prove that: log sin8x=3log2+log sin x+log cos2x+log cos4x

int (dx)/(1 + tan x) is equal to a) (1)/(2) + (1)/(2)log|cos x + sin x|+C b) (x)/(2) + (1)/(2) log|cos x - sin x| +C c) (1)/(2) + (1)/(2) log|cos x - sin x| + C d) (x)/(2) + (1)/(2) log|cos x + sin x| + C

int sin log x+cos log x]backslash dx is equal to

For 0 lt x lt (pi)/(2) , let P_(mn)(x)=m log_(cos x) ( sin x)+ n log_(cos x)(cotx) , where m, n in {1, 2,...,9} [For example: P_(29)(x)=2log_(cosx)(sinx)+9log_(cos x)( cot x) and " " P_(77)(x)=7 log_(cos x)(sin x)+(7 log_(cos x) ( cot x) ] On the basis of above information, answer the following questions : If P_(34)(x)=P_(22)(x) , then the value of sin x is expressed as ((sqrt(q)-1)/(p)) , then (p+q) equals

For 0 lt x lt (pi)/(2) , let P_(mn)(x)=m log_(cos x) ( sin x)+ n log_(cos x)(cotx) , where m, n in {1, 2,...,9} [For example: P_(29)(x)=2log_(cosx)(sinx)+9log_(cos x)( cot x) and " " P_(77)(x)=7 log_(cos x)(sin x)+(7 log_(cos x) ( cot x) ] On the basis of above information, answer the following questions : If P_(34)(x)=P_(22)(x) , then the value of sin x is expressed as ((sqrt(q)-1)/(p)) , then (p+q) equals

For 0 lt x lt (pi)/(2) , let P_(mn)(x)=m log_(cos x) ( sin x)+ n log_(cos x)(cotx) , where m, n in {1, 2,...,9} [For example: P_(29)(x)=2log_(cosx)(sinx)+9log_(cos x)( cot x) and " " P_(77)(x)=7 log_(cos x)(sin x)+(7 log_(cos x) ( cot x) ] On the basis of above information, answer the following questions : If P_(34)(x)=P_(22)(x) , then the value of sin x is expressed as ((sqrt(q)-1)/(p)) , then (p+q) equals

For 0 lt x lt (pi)/(2) , let P_(mn)(x)=m log_(cos x) ( sin x)+ n log_(cos x)(cotx) , where m, n in {1, 2,...,9} [For example: P_(29)(x)=2log_(cosx)(sinx)+9log_(cos x)( cot x) and " " P_(77)(x)=7 log_(cos x)(sin x)+(7 log_(cos x) ( cot x) ] On the basis of above information, answer the following questions : If P_(34)(x)=P_(22)(x) , then the value of sin x is expressed as ((sqrt(q)-1)/(p)) , then (p+q) equals