Question

plse solve it plse
plse plse plse​

Answer 1

Answer:

proved solution in attached pic

Step-by-step explanation:

Given Tan A values

we first assume a right angle triangle

then accordingly with the given sides

we find the hypotenuses by using Pythagoras theorem and then substitute in place of Sin A and Cos A

we get the desired result by rationalization

please check the solution pic for clarity.

Answer 2

Answer:

Proved

Step-by-step explanation:

tanA = √2  - 1

tanA = SinA / CosA

SinA/CosA = √2  - 1

Squaring both sides

Sin²A/Cos²A = 2 + 1 - 2√2

=> Sin²A = Cos²A (3 - 2√2)

=> 1 - Cos²A = Cos²A(3 - 2√2)

=> Cos²A ( 1 + 3 - 2√2)  = 1

=> Cos²A = 1/(4 - 2√2)

Sin²A = 1 - Cos²A

=> Sin²A = 1 - 1/(4 - 2√2)

=> Sin²A = (3 - 2√2)/(4 - 2√2)

Sin²ACos²A = (3 - 2√2)/(4 - 2√2)  × 1/(4 - 2√2)

=> Sin²ACos²A =  (3 - 2√2) / ( 16 + 8 - 16√2)

=> Sin²ACos²A =  (3 - 2√2) / ( 24 - 16√2)

=> Sin²ACos²A =  (3 - 2√2) / ( 8 ×( 3 - 2√2))

=> Sin²ACos²A = 1/8

Square rooting both sides

=> SinACosA = ± 1/(2√2)

Multiplying numerator & denominator by √2

=> SinACosA =  ± √2/4

QED ( Hence Proved)