Additional Math – Trigonometry – Proving Identities

image: amath solution to trigonometry proving identities of sine cosine and tangent

Sunday Additional Math Group Tuition at Woodlands – prove identities trigonometry

$latex \displaystyle \text{LHS}$
$latex \displaystyle {{\sec }^{4}}x-{{\tan }^{4}}x$
Factorizing using  the algebraic special products a2-b2=(a+b)(a-b).
$latex \displaystyle {{\left( {{{{\sec }}^{2}}x} \right)}^{2}}-{{\left( {{{{\tan }}^{2}}x} \right)}^{2}}$
$latex \displaystyle \left( {{{{\sec }}^{2}}x+{{{\tan }}^{2}}x} \right)\left( {{{{\sec }}^{2}}x-{{{\tan }}^{2}}x} \right)$
Use the trigonometry formula sec2x=1+tan2x.
$latex \displaystyle \left( {1+{{{\tan }}^{2}}x+{{{\tan }}^{2}}x} \right)\left( {1+{{{\tan }}^{2}}x-{{{\tan }}^{2}}x} \right)$
$latex \displaystyle \left( {1+2{{{\tan }}^{2}}x} \right)\left( 1 \right)$
Change the expression by making cos2x the common denominat.
$latex \displaystyle \frac{{{{{\cos }}^{2}}x}}{{{{{\cos }}^{2}}x}}+2\frac{{{{{\sin }}^{2}}x}}{{{{{\cos }}^{2}}x}}$
$latex \displaystyle \frac{{{{{\cos }}^{2}}x+2{{{\sin }}^{2}}x}}{{{{{\cos }}^{2}}x}}$
$latex \displaystyle \frac{{{{{\cos }}^{2}}x+{{{\sin }}^{2}}x+{{{\sin }}^{2}}x}}{{{{{\cos }}^{2}}x}}$
Simplify the expression.
$latex \displaystyle \frac{{1+{{{\sin }}^{2}}x}}{{{{{\cos }}^{2}}x}}$
$latex \displaystyle \text{LHS=RHS}$

Always start with the side that looks more complicated. For this case, it is the left hand side. Place the N/O Level formula sheet beside you, look at the trigonometry formula while solving the trigonometric identities.

Trigonometric Identities in one of the most challenging sub-topics in Additional Math. But regular practice will give you confidence and help you solve quickly and correctly.

Additional Math (amath) trigonometry identities. Students from Woodlands, Choa Chu Kang, Yew Tee, Sembawang and Yishun.


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