Question

(Sec2A-1)(1-cosec2A)=K
Find k with proper xplanation..... plzz

Answer 1

(Sec2A-1)(1-cosec2A)=K

$[\frac{1}{Cos2A}-1][1-\frac{1}{Sin2A}]$=K

$\frac{1-Cos2A}{Cos2A}\times\frac{Sin2A-1}{Sin2A}$=K

Using the identity, Cos2A=2Cos²A-1=1-2Sin²A=Cos²A-Sin²A, Sin2A=2 SinA CosA,Sin2A-1= -(CosA-SinA)²or -(SinA-CosA) and substituting in above equation

$\frac{2Sin^{2}A\times-(CosA-SinA)^{2}}{Cos2A\times2SinACosA}$=K

As Cos2A=Cos²A-Sin²A=[CosA-SinA][CosA+SinA]

The above equation get reduced to

$\frac{Sin A}{CosA}\times\frac{CosA-SinA}{CosA+SinA} or \frac{Sin A}{CosA}\times\frac{SinA-CosA}{CosA+SinA}$=K

$tanA\times\frac{1-tanA}{1+tanA} or tanA\times\frac{tanA-1}{1+tanA}$=K→Dividing numerator and denominator by CosA

As ,tan(π/4)=1 and use tan [π/4+A]=$\frac{1+tanA}{1-tanA}$

and tan[A-π/4]=$\frac{tanA-1}{tanA+1}$

K=$tanA\times tan[A+\frac{\pi}{ 4}] or tanA\times tan[A-\frac{\pi}{ 4}]$

Answer 2

Answer:

Step-by-step explanation:sec2A-1 *1-cosec2a=-1