Question

(1+cotA - cosecA)(1+ tanA +secA)​

Answer 1

Step-by-step explanation:

cosecA=1/sinA

secA=1/cosA

And cotA=(cosA/sinA)

tanA=(sinA/cosA)

So substituting value and taking LCM we get

(sinA+cosA-1)(cosA+sinA+1)/sinAcosA

Now (a+b)(a-b)=a^2-b^2

So

((sinA+cosA)^2–1)/sinAcosA

(sin^2A+2sinAcosA+cos^2A-1)/sinAcosA

Now sin^2A+cos^2A=1 SO….

2sinAcosA/sinAcosA=2

And=2

Hope you get it :)

Answer 2

Answer:

2

Step-by-step explanation:

= $(1 + \frac{sinA }{cosA } + \frac{1}{cosA}) (1 + \frac{cosA}{sinA} -\frac{1}{sinA})$

= $(\frac{cosA+sinA+1}{cosA} )(\frac{sinA+cosA-1}{sinA} )$

= $\frac{(cosA+sinA)^{2}-1^{2} }{sinAcosA}$

$= \frac{cos^{2}A + sin^{2}A + 2sinAcosA - 1}{sinAcosA}$

$= \frac{1+2sinAcosA-1}{sinAcosA}$

$= \frac{2sinAcosA}{sinAcosA} = 2$   (answer)