Question

if x+y = 90
Sec2x- Cot2y = 1​

Answer 1

SOLUTION

GIVEN

x + y = 90°

TO PROVE

$\sf{ { \sec}^{2} x - { \cot}^{2}y = 1 }$

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric formula that

$\sf{ { \sec}^{2} \theta - { \tan}^{2} \theta = 1 }$

EVALUATION

Here it is given that x + y = 90°

∴ y = 90° - x

Now

$\sf{ { \sec}^{2} x - { \cot}^{2}y }$

$\sf{ = { \sec}^{2} x - { \cot}^{2}( {90}^{ \circ} - x) }$

$\sf{ = { \sec}^{2} x - \bigg[{ \cot( {90} ^{ \circ} - x) \bigg] }^{2} }$

$\sf{ = { \sec}^{2} x - \bigg[{ \tan x \bigg] }^{2} }$

$\sf{ = { \sec}^{2} x - { \tan}^{2} x }$

$= 1$

Hence proved

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