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Proposed by Langlands, the 'beyond endoscopy' method provides a way to study functoriality through its analytic properties. One important example is worked out by Venkatesh, who classified the dihedral forms as the presence of a pole in its symmetric square lift. This approach relies on the idea that the trace formula alone is sufficiently robust to reveal functoriality. In this talk, we will discuss the following two works within this philosophy. The first is proof of the GL(2) functional equation via the trace formula. Joint with Chung-Hang Kwan, we discovered a novel character sum identity that acts as a reciprocity relation. The framework of proof is also parallel with how various spectral reciprocity identities are established. The second one is a joint work with Valentin Blomer, where we proved the GL(3) converse theorem via GL(3) Kuznetsov trace formula.