Question

The value of (1+cotA-cosecA)(1+tanA+secA) is:​

Answer 1

Answer: 2

Step-by-step explanation:

cosecA=1/sinA  

secA=1/cosA  

And cotA=(cosA/sinA)

tanA=(sinA/cosA)

(sinA+cosA-1)(cosA+sinA+1)/sinAcosA  

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

((sinA+cosA)^2–1)/sinAcosA  

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

sin^2A+cos^2A=1  

2sinAcosA/sinAcosA=2

=2

Answer 2

$(1 + cota - coseca)(1 + tana + cota) \\ \\ = ( \frac{sina + cosa - 1}{sina} )( \frac{cosa + sina + 1}{cosa} ) \\ \\ = \frac{( {sina + cosa)}^{2} - 1 }{sinacosa} \\ \\ = \frac{2sinacosa}{sinacosa} \\ \\ = 2$