Question

Give me correct answer​

Answer 1

Answer:

Refer to attachment

Third step Explanation:

${ \sf{We \: know \: that, { \boxed{{cos}^{2}A - {sin}^{2} A = cos2A}} }} \\ \\ : { \implies{ \sf{ {cos}^{2} \frac{ \theta}{2} - {sin}^{2} \frac{ \theta}{2} = cos2 \bigg( \frac{ \theta}{2} \bigg) }}} \\ \\ : { \implies{ \sf{{cos}^{2} \frac{ \theta}{2} - {sin}^{2} \frac{ \theta}{2} =cos \cancel{2} \bigg( \frac{ \theta}{ \cancel{{2}}} \bigg) }}} \\ \\ : { \implies{ \sf{{cos}^{2} \frac{ \theta}{2} - {sin}^{2} \frac{ \theta}{2} = cos \theta}}}$

More identities:

↦ sin² A + cos² A = 1

↦ cos²A - Sin²A = Cos2A

↦ 1+tan² A = sec² A

↦ cosec² A = 1 + cot² A

Answer 2

tan

(

θ

2

)

+

cot

(

θ

2

)

=  

sin

(

θ

2

)

cos

(

θ

2

)

+

cos

(

θ

2

)

sin

(

θ

2

)

=  

sin

2

(

θ

2

)

+

cos

2

(

θ

2

)

sin

(

θ

2

)

cos

(

θ

2

)

=  

1

sin

(

θ

2

)

cos

(

θ

2

)

=  

2

2

sin

(

θ

2

)

cos

(

θ

2

)

=  

2

sin

θ

=  

2

csc

θ