Question

in intriangle abc right angled at a is a b equal 24 cm and ac equal to 7 cm find all trigonometric ratios of Angle B and verify the result sec square B minus tan b​

Answer 1

Answer:

Sin B = 7/25, Cos B 24/25, Tan B = 7/24, Cot B = 24/7, Sec B = 25/24, Cosec B = 25/7

$Sec^{2}$ B - $Tan^{2}$ B = 1

Step-by-step explanation:

Given that;

ABC is a right-angled Triangle. ∠A = $90^{o}$

Refer to the figure at the attachment.

From the figure ABC,

$(BC)^{2}$ = $(AB)^{2}$ + $(AC)^{2}$ (Pythogoras Theorem)

                            = $(24)^{2}$ + $(7)^{2}$ (Given; AB = 24, AC = 7)

$(BC)^{2}$ = 625

=> BC = $\sqrt{625}$ = 25

Trigonometric Ratios of ∠B:

Sin B = Perpendicular/Hypotenuse

Cos B = Base/Hypotenuse

Tan B = Sin B/Cos B = Perpendicular/Base

Cot B = Cos B/Sin B = Base/Perpendicular

Sec B = 1/Cos B = Hypotenuse/Base

Cosec B = 1/Sin B = Hypotenuse/Perpendicular

Sin B = 7/25

Cos B = 24/25

Tan B = 7/24

Cot B = 24/7

Sec B = 25/24

Cosec B = 25/7

Also,

$Sec^{2}$ B - $Tan^{2}$ B = $(25/24)^{2}$ - $(7/24)^{2}$

                                   = (625 - 49)/$24^{2}$

                                   = 576/(24 x 24)

                                   = 1