Let x=2( log 2 3)( log 3 4) ldots ldots ldots, where the last term in exponent is log 99 100, then the value of cos ((x π/4))+ sin ((x π/4)) is equal to

Question

Let x=2( log 2 3)( log 3 4) ldots ldots ldots, where the last term in exponent is log 99 100, then the value of cos ((x π/4))+ sin ((x π/4)) is equal to (A) 1 (B) (1/√2) (C) √2 (D) -1

Tardigrade Admin · Accepted Answer

2 log 2 3 × log 3 4 × ldots × log 99 100=2 log 2 100=100 ∴ cos (x π/4)+ sin (x π/4)= cos 25 π+ sin 25 π=-1

Q. Let $x = 2^{(l o g_{2} 3) (l o g_{3} 4) \dots\dots\dots}$ , where the last term in exponent is $lo g_{99} 100$ , then the value of $cos (\frac{x π}{4}) + sin (\frac{x π}{4})$ is equal to

1

$\frac{1}{2}$

$2$

-1

$2^{l o g_{2} 3 \times l o g_{3} 4 \times \dots \times l o g_{99} 100} = 2^{l o g_{2} 100} = 100$
$∴ cos \frac{x π}{4} + sin \frac{x π}{4} = cos 25 π + sin 25 π = - 1$

Q. Let x=2(log2​3)(log3​4)………, where the last term in exponent is log99​100, then the value of cos(4xπ​)+sin(4xπ​) is equal to

1

2​1​

2​

-1

2log2​3×log3​4×…×log99​100=2log2​100=100 ∴cos4xπ​+sin4xπ​=cos25π+sin25π=−1

Q. Let $x = 2^{(l o g_{2} 3) (l o g_{3} 4) \dots\dots\dots}$ , where the last term in exponent is $lo g_{99} 100$ , then the value of $cos (\frac{x π}{4}) + sin (\frac{x π}{4})$ is equal to

$\frac{1}{2}$

$2$

$2^{l o g_{2} 3 \times l o g_{3} 4 \times \dots \times l o g_{99} 100} = 2^{l o g_{2} 100} = 100$
$∴ cos \frac{x π}{4} + sin \frac{x π}{4} = cos 25 π + sin 25 π = - 1$